By Newton's second law, the net force on the object is
∑ F = m a
∑ F = (2.00 kg) (8 i + 6 j ) m/s^2 = (16.0 i + 12.0 j ) N
Let f be the unknown force. Then
∑ F = (30.0 i + 16 j ) N + (-12.0 i + 8.0 j ) N + f
=> f = (-2.0 i - 12.0 j ) N
QUESTION 16
When the BOTTLE is squeezed, when a bottle with a reservoir is squeezed, which statement will be true?
The tube will fill the reservoir with liquid from the bottle.
The tube will suck liquid from the reservoir into the bottle.
The fluid will drain from the reservoir to the rest of the bottle.
The fluid will come up through the bottom of the reservoir.
Answer:
20 characters
Explanation:
The bottle is squeezed, when a bottle with a reservoir is squeezed, is the fluid will come up through the bottom of the reservoir. Thus, the correct option is D.
What is a reservoir?A reservoir is an artificial lake where the water is stored. Most of the reservoirs are formed through the construction of the dams across major rivers. A reservoir can also be formed from a natural lake whose outlet has been dammed to control the water level in that.
When we squeeze an open bottle which is filled with water, the water in the bottle will spill out. When we squeeze a bottle, the material collapses where we squeeze it, however it expands in other areas, resulting in a constant volume. If the volume is constant, then we would think that the water should not spill out.
Therefore, the correct option is D.
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A child sleds down a snowy hillside starting from rest. The hill has a 15 degree slope, with a long stretch of level field at the foot. The child starts 50 ft up the slope and continues for 100 ft on the level field before coming to a complete stop. Find the coefficient of friction between the sled and the snow, assuming that it is constant throughout the ride. Neglect air resistance.
Answer:
0.0872
Explanation:
the solution to the problem can be found in the attachment section. Please go through and feel free to ask your doubts.
How many x-ray photons per second are created by an x-ray tube that produces a flux of x rays having a power of 1.00 W
Complete question:
How many x-ray photons per second are created by an x-ray tube that produces a flux of x rays having a power of 1.00 W. Assume the average energy per photon in 78.0 keV.
Answer:
The number of x-ray photons per second created by the x-ray tube is 8.01 x 10¹³ photons/sec
Explanation:
Given;
power of the flux produced, P = 1 W = 1 J/s
energy per photon, E = 78 keV
Convert the energy per photon to J
E = 78 x 10³ x 1.6 x 10⁻¹⁹ = 1.248 x 10⁻¹⁴ J / photon
let the number of photons = n
n(1.248 x 10⁻¹⁴ J / photon) = 1 J/s
[tex]n = \frac{1 \ J/s}{1.248 \times 10^{-14}\ J/photon } = 8.01 \times 10^{13} \ photons/s[/tex]
Therefore, the number of x-ray photons per second created by the x-ray tube is 8.01 x 10¹³ photons/sec
A 9.2 resistor and a 5.2 resistor are connected in series with a battery. The potential difference across the 5.2 resistor is measured as 12 V. Find the potential difference across the battery.
Answer:
V = 33.12 V
Explanation:
Given that,
A 9.2 resistor and a 5.2 resistor are connected in series with a battery.
The potential difference across the 5.2 resistors is measured as 12 V.
In series combination of resistors, the current is same throughout the circuit. Let I is the current. Using Ohm's law,
[tex]I=\dfrac{V}{R}[/tex]
Put all the values,
[tex]I=\dfrac{12}{5.2}\\\\I=2.30\ A[/tex]
The equivalent resistance is :
R = 9.2 + 5.2
= 14.4 ohms
Let V os the potential difference across the battery. So,
[tex]V=2.3\times 14.4\\\\V=33.12\ V[/tex]
So, the potential difference across the battery is equal to 33.12 V.
At noon, ship A is 140 km west of ship B. Ship A is sailing east at 30 km/h and ship B is sailing north at 25 km/h. How fast (in km/hr) is the distance between the ships changing at 4:00 p.m.
Answer:
The rate of change of distance between the two ships is 18.63 km/h
Explanation:
Given;
distance between the two ships, d = 140 km
speed of ship A = 30 km/h
speed of ship B = 25 km/h
between noon (12 pm) to 4 pm = 4 hours
The displacement of ship A at 4pm = 140 km - (30 km/h x 4h) =
140 km - 120 km = 20 km
(the subtraction is because A is moving away from the initial position and the distance between the two ships is decreasing)
The displacement of ship B at 4pm = 25 km/h x 4h = 100 km
Using Pythagoras theorem, the resultant displacement of the two ships at 4pm is calculated as;
r² = a² + b²
r² = 20² + 100²
r = √10,400
r = 101.98 km
The rate of change of this distance is calculated as;
r² = a² + b²
r = 101.98 km, a = 20 km, b = 100 km
[tex]2r(\frac{dr}{dt} ) = 2a(\frac{da}{dt} ) + 2b(\frac{db}{dt} )\\\\r(\frac{dr}{dt} ) = a(\frac{da}{dt} ) + b(\frac{db}{dt} )\\\\101.98(\frac{dr}{dt} ) = 20(-30 ) + 100(25 )\\\\101.98(\frac{dr}{dt} ) = -600 + 2,500\\\\101.98(\frac{dr}{dt} ) = 1900\\\\\frac{dr}{dt} = \frac{1900}{101.98} = 18.63 \ km/h[/tex]
Which object has the most gravitational potential energy?
O A. A 5 kg book at a height of 2 m
B. A 8 kg book at a height of 2 m
C. An 8 kg book at a height of 3 m
D. An 5 kg book at a height of 3 m
help pls
Answer: An 8 kg book at a height of 3 m has the most gravitational potential energy.
Explanation:
Gravitational potential energy is the product of mass of object, height of object and gravitational field.
So, formula to calculate gravitational potential energy is as follows.
U = mgh
where,
m = mass of object
g = gravitational field = [tex]9.81 m/s^{2}[/tex]
h = height of object
(A) m = 5 kg and h = 2m
Therefore, its gravitational potential energy is calculated as follows.
[tex]U = mgh\\= 5 kg \times 9.81 m/s^{2} \times 2 m\\= 98.1 J (1 J = kg m^{2}/s^{2})[/tex]
(B) m = 8 kg and h = 2 m
Therefore, its gravitational potential energy is calculated as follows.
[tex]U = mgh\\= 8 kg \times 9.81 m/s^{2} \times 2 m\\= 156.96 J (1 J = kg m^{2}/s^{2})[/tex]
(C) m = 8 kg and h = 3 m
Therefore, its gravitational potential energy is calculated as follows.
[tex]U = mgh\\= 8 kg \times 9.81 m/s^{2} \times 3 m\\= 235.44 J (1 J = kg m^{2}/s^{2})[/tex]
(D) m = 5 kg and h = 3 m
Therefore, its gravitational potential energy is calculated as follows.
[tex]U = mgh\\= 5 kg \times 9.81 m/s^{2} \times 3 m\\= 147.15 J (1 J = kg m^{2}/s^{2})[/tex]
Thus, we can conclude that an 8 kg book at a height of 3 m has the most gravitational potential energy.
Which of the following is an example of potential energy?
Answer:
C.
Explanation:
Kinetic Energy is defined as something that possesses energy because it is in motion. Potential Energy is something that is at rest that ha the potential to have kinetic energy when it is set in motion.
All of these other choices are in motion, hence, they have kinetic energy. The jar is at rest, so it has potential energy. All of those objects were are rest at one point and had kinetic energy, before they started moving. If the jar was to fall off the shelf, its potential energy would transfer to kinetic energy.
Answer:
C. Glass jar sitting of a shelf
Explanation:
Because everything else is full of kinetic energy but moving, so the only item not using kinetic energy is the jar.
what are the laws of Physics
Answer:
thermodynamics
Explanation:
The laws of thermodynamics define a group of physical quantities, such as temperature, energy, and entropy, that characterize thermodynamic systems in thermodynamic equilibrium.
Compare the percent change in angular momentum of the system to the percent change in the rotational kinetic energy of the system. Explain the difference between these two values.
Answer:
change in the angular momentum gives a greater change in the kinetic energy since it has a quadratic dependence with the angular velocity
Explanation:
Let's write the definition of angular momentum
L = I w
the kinetic energy is
K = ½ I w²
w = L / I
we substitute
K = ½ I L² / I²
K = L² / 2I
K / L = w / 2
therefore a change in the angular momentum gives a greater change in the kinetic energy since it has a quadratic dependence with the angular velocity
What is the resistance a circult when 9V batter is connected the circult to generate 0.002A
Answer:
v= IR then you can R= v/I 9v÷0.002 = 450 Ohms
The organ that functions to pull in oxygen and release carbon
dioxide gases.
Answer:
lungs. hopes this helps
Air in a thundercloud expands as it rises. If its initial temperature is 292 K and no energy is lost by thermal conduction on expansion, what is its temperature when the initial volume has tripled
Answer:
Explanation:
It is a case of adiabatic expansion .
[tex]T_1V_1^{\gamma-1}=T_2V_2^{\gamma-1}[/tex]
T₁ , T₂ are initial and final temperature , V₁ and V₂ are initial and final volume.
Given ,
V₂ = 3 V₁ and T₁ = 292 . γ for air is 1.4 .
[tex]( 3 )^{\gamma-1}= \frac{292}{ T_2}[/tex]
[tex]( 3 )^{1.4-1}= \frac{292}{ T_2}[/tex]
1.552 = 292 / T₂
T₂ = 188 K .
What is the momentum of a lab cart with a mass of 0.60 [kg] and a speed of 2.2 [m/s]?
-3.67 [kg m/s)
-0.27 [kg m/s]
-1.32 [kg m/s)
-0.82 [kg m/s)
Answer:
1.32kgm/s
Explanation:
use the formula: p=mv
The momentum of a lab cart = -1.32 kg m/s
What is momentum?It is measure of the inertia of a body/ object .It can be calculated by multiplying mass with velocity .
General formula for momentum = M = m * v
given
mass = 0.60 kg
speed = 2.2 m/s
velocity = - 2.2 m/s ( answer is in negative , since mass is a scaler quantity but velocity is a vector quantity hence , velocity can be negative )
momentum = mass * velocity
= 0.60 * (-2.2 ) = -1.32 kg m/s
The momentum of a lab cart =c) -1.32 kg m/s
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When you press on a circular table of radius 0.5 m, with a force of 20N, what will be exerted pressure?
50pa
25pa
40N/m
10N.m
Answer and I will give you brainiliest
Answer:
Note the word "circular".
Meaning the area would be found using that of a circle = πr²
Recall
Pressure = Force/Area
Area = π x 0.5² = 0.785m²
Pressure = 20/0.785
= 25pa ( to the nearest whole number)
Pressure = Force/Area
From the question,we have force ryt? so now let's find the area.As the table is circular, we have to use the formula of area of circle;
= πr²
= 3.14 × 0.5 × 0.5
= 3.14 × 0.25
= 0.785 m²
Put the values of force and area in formula;
= 20/0.785
= 20000/785
= 25.45 Pa
= 25 Pa (Approx)
Charge q is a test charge used to measure the electric field created by a source charge Q. What happens to the magnitude of the electric force on these charges if q is doubled?
Answer:
The electric force will also double.
When the test charge q is double the change in magnitude of the electric force is that it also gets doubled.
What is the electric force due to charge?Electric force is defined as force between the chages which is directly proportional to the product of charges and inversely proportional to the square of the distance between them. The electric force is a vector quantity, It have magnitude as well as direction.
Electric force = k*Q*q/r²
The electric field is defined as the electric force per unit charge. The electric field is a vector quantity.
Electric field = Electric force / test charge
Electric field = k*Q/r²
Given that in question there is the test charge, q for electric field and the source charge Q when the test charge q will become 2q then electric force is,
Electric force = kQ(2q)/r²
So, the magnitude of the electric force is increased by twice when the test charge will become 2q.
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Chuck and Jackie stand on separate carts, both of which can slide without friction. The combined mass of Chuck and his car, mcartmcart, is identical to the combined mass of Jackie and her cart. Initially, Chuck and Jackie and their carts are at rest.
Chuch then picks up a ball of mass mballmball and throws it to Jackie, who catches it. Assume that the ball travels in a straight line parallel to the ground (ignore the effect of gravity). After Chuck throws the ball, his speed relative to the ground is vc. The speed of the thrown ball relative to the ground is vb. Jackie catches the ball when it reaches her, and she and her cart begin to move. Jackie's speed relative to the ground after she catches the ball is vj.
When answering the questions in this problem, keep the following in mind:
1. The original mass mcartmcart of Chuck and his cart does not include the mass of the ball.
2. The speed of an object is the magnitude of its velocity. An object's speed will always be a non-negative quantity.
Required:
a. Find the relative speed u between Chuck and the ball after Chuck has thrown the ball.
b. What is the speed vb of the ball (relative to the ground) while it is in the air?
c. What is Chuck's speed vc (relative to the ground) after he throws the ball?
d. Find Jackie's speed vj (relative to the ground) after she catches the ball in terms of vb.
e. Find Jackie's speed vj (relative to the ground) after she catches the ball in terms of u.
Explanation:
a.)
We find the relative speed
u = vb + vc
b.)
chuck and the cart are at a rest position
mcartvc = mballvb
from part a above,
vc = u - vb
mcartu = vb(mcart + mball)
make vb the subject of the equation
[tex]vb=\frac{mcartu}{mcart +mball}[/tex]
c.)
from anser a,
vb = u - vc
then mcart vc = mball(u-vc)
[tex]vc= \frac{Mballu}{Mcart+Mball}[/tex]
d.
Mballvb = (Mcart + Mball)vj
we make vj the subject to get her relative speed
[tex]vj=\frac{MballVb}{Mcart+Mball}[/tex]
e.
given the solution in part d above,
we have
[tex]vj=\frac{MballVb}{Mcart+Mball}[/tex]
remember,
vb = u - vc
such that
[tex]Vj = \frac{Mball(u-v)}{Mball +Mcart}[/tex]
thank you!
If an EM wave has a wavelength of 595 nm, what is its frequency?
5.02 x 10^5 s
1.99 x 10^-6 Hz
5.02 x 10^14 Hz
1.99 x 10^-15 s
None of the above
Explanation:
1.9If an EM wave has a wavelength of 595 nm, what is its frequency9 x 10^-6 Hz
Explanation:
aah cmmon just come over to my meet
The Starship Enterprise returns from warp drive to ordinary space with a forward speed of 54 km/s . To the crew's great surprise, a Klingon ship is 110 km directly ahead, traveling in the same direction at a mere 22 km/s. Without evasive action, the Enterprise will overtake and collide with the Klingons in just about 3.4 s. The Enterprise's computers react instantly to brake the ship. What magnitude acceleration does the Enterprise need to just barely avoid a collision with the Klingon ship?
Answer:
The acceleration will be "-5.12 km/s²".
Explanation:
The given values are:
This might be defined as a continuous inanimate object at either the speed between such organization as well as the Klingon boat (54 - 22) km/s.
The values given in the question are:
= 110 km
Final velocity will be:
= 0
By using to the third equation of motion, we get
⇒ [tex]v^2=u^2+2as[/tex]
[tex]0=(54-22)^2+2\times a\times 100[/tex]
[tex]0=(32)^2+2\times a\times 100[/tex]
[tex]0=1024+2\times a\times 100[/tex]
[tex]0=1024+200a[/tex]
[tex]-1024=200a[/tex]
[tex]a=-\frac{1024}{200}[/tex]
[tex]=-5.12 \ km/s^2[/tex]
In some situations, matter demonstrates wave behavior rather than particle behavior. This is best illustrated by which phenomenon? A. Emission spectra of atoms B. Blackbody radiation C. Interference patterns of electrons D. Photoelectric effect
Answer:
In some situations, matter demonstrates wave behavior rather than particle behavior. This is best illustrated by which phenomenon is:
C. Interference patterns of electrons.
Answer:
C. Interference patterns of electrons
If a cat can exert 2000N Of Force to move a trailer 50m is 20 seconds how much power did the car use ?
им putins брат, почему вы обманываете нашу систему образования, Это теперь запрещено в России.
How do solar systems, galaxies, and the universe show different frames of reference about space?
Answer:
Many people are not clear about the difference between our Solar System, our Milky Way Galaxy, and the Universe.
Let’s look at the basics.
Our Solar System consists of our star, the Sun, and its orbiting planets (including Earth), along with numerous moons, asteroids, comet material, rocks, and dust. Our Sun is just one star among the hundreds of billions of stars in our Milky Way Galaxy. If we shrink the Sun down to smaller than a grain of sand, we can imagine our Solar System to be small enough to fit onto the palm of your hand. Pluto would orbit about an inch from the middle of your palm.
Artist diagram of Milky Way galaxy
On that scale with our Solar System in your hand, the Milky Way Galaxy, with its 200 – 400 billion stars, would span North America (see the illustration on the right). Galaxies come in many sizes. The Milky Way is big, but some galaxies, like our Andromeda Galaxy neighbor, are much larger.
The universe is all of the galaxies – billions of them! NASA’s telescopes allow us to study galaxies beyond our own in exquisite detail, and to explore the most distant reaches of the observable universe. The Hubble Space Telescope made one of the deepest images of the universe, called the Hubble Extreme Deep Field (image at the top of this article). Soon the James Webb Space Telescope will be exploring galaxies forming at the very beginning of the universe.
You are one of the billions of people on our Earth. Our Earth orbits the Sun in our Solar System. Our Sun is one star among the billions in the Milky Way Galaxy. Our Milky Way Galaxy is one among the billions of galaxies in our Universe. You are unique in the Universe!
You can observe objects in our solar system and even see other galaxies at a star party near you-and rest assured that everything you are seeing is a part of the same universe as you!
Explanation:
A solar system is the system of celestial bodies built around a central star, the Sun. All of the system bodies, be they dwarf planets, small bodies and large planets, are held in a gravitational bond around the central star. Our solar system has eight large planets:
Four inner planets which are terrestrial, made entirely of rock and metal: Mars, Mercury, Earth and Venus;
Four outer planets which are gas and ice giants: Jupiter and Saturn (composed entirely of helium and hydrogen), Uranus and Neptune (composed of ices such as water, ammonia and methane).
The solar system also contains asteroid belts and the natural satellites of some of the planets. The trans-Neptunian region has the Kuiper belt, home to several dwarf planets, Pluto among them. Our solar system is located on the Orion Arm and is part of the Milky Way Galaxy. It was formed 4.6 billion years ago.
A galaxy is made out of billions of stars and their solar systems, held together by gravity, with a super- massive black hole at the center. Our Solar System is called the Milky Way; it is a spiral galaxy and the black hole in the center is called Sagittarius A*. Apart from the spiral shape, galaxies can also be elliptical or irregular in form. Galaxies gather in groups, clusters and super-clusters and there are billions of Galaxies in the Universe.
Some of these other galaxies are visible to the naked eye on a dark night and from places away from artificial light sources. The Andromeda Galaxy is the most recorded one throughout time and all over the world, its existence having been noted since the 10th century by Persian astronomer Al-Sufi, and having been the object of debate among other great thinkers up to the moment when the technology caught up to the discourse.
Solar System vs Galaxy
So what is the difference between a solar system and a galaxy?
A solar system represents the group of planets gravitationally bound to the central star. A galaxy has billions of stars and their solar systems. This difference in size is not only visible in the number of stars it is made out of, but also by how long it takes to cross it. It takes one light year to cross our solar system, and 100,000 light years to cross the galaxy.
While the biggest thing inside a solar system is the central sun, the biggest thing inside a galaxy is a massive black hole. The planets in a solar system orbit the sun, which is at the center, and the Sun, in turn, orbits the center of the Milky Way.
Comparison Chart
Solar system Galaxy
A group of planets orbiting the central sun A group of planetary systems whose central Suns are orbiting the center of the Galaxy
Gravitationally bound Gravitationally bound
Can be crossed in 1 light year Can be crossed in 100,000 light years
Most of the system mass is taken up by the central sun It hosts a super massive black hole, Sagittarius A*
More solar systems make up galaxies More galaxies make up the Universe
A deer with a mass of 156 kg is running head on toward you with a speed of 10 m/s. Find the momentum of the deer
Hi there!
[tex]\large\boxed{1560 kgm/s}[/tex]
Recall that:
P = m · v, where:
P = momentum
m = mass (kg)
v = velocity (m/s)
Thus:
P = 156 · 10
P = 1560 kgm/s
Please helppppppp!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
I think the Bulb No. 2 will stop emitting light if the bulb No. 1 burns out.
Determine the binding energy of an F-19 nucleus. The F-19 nucleus has a mass of 18.99840325 amu. A proton has a mass of 1.00728 amu, a neutron has a mass of 1.008665 amu, and 1 amu is equivalent to 931 MeV of energy. Group of answer choices
Answer:
Energy = 1.38*10^13 J/mol
Explanation:
Total number of proton in F-19 = 9
Total number of neutron in F-19 = 10
Expected Mass of F-19
= 9*1.007 + 10*1.008 = 19.152 u
Actual mass of F-19 = 18.998 u
Energy of one particle of F-19 = 931.5*Δm = 931.5*(19.152-18.998)
= 143.234 MeV
Energy of one mole of F-19 = 143.234*10^6*1.6*10^-19*6.022*10^23
= 1.38*10^13 J/mol
Your tutor says atomic nuclei are converted to nuclear energy in a nuclear reaction. why should you seek a new tutor?
Answer:
The answer is "Momentum and net Energy(that contains mass)".
Explanation:
No matter which type of nuclear reaction, the momentum always is maintained. According to the formula, E = mc^2 of Einstein, energy conservation on the atomic level requires the change in mass of its core which may have been shared throughout the reaction as mass and energy, that's why we can say that the nuclei aren't fully converted into electrical energy rather rearranged and the mass could be changed and dispensed to the nucleon as energy.
A good soccer player can kick the ball up to 25 m/sec. A soccer ball has a mass of 800 grams (0.8 kg). What force must a goalie exert on the ball to bring it to rest in 0.1 sec?
Answer:
200 N
Explanation:
Applying,
The force a golie must exert on the ball is,
F = ma...................... Equation 1
Where m = mass of the ball, a = acceleration of the ball.
But,
a = Δv/t............... Equation 2
Where Δv = change in velocity, t = time.
Substitute equation 2 into equation 1
F = m(Δv/t)............... Equation 3
From the question,
Given: m = 0.8 g, t = 0.1 s, Δv = 25 m/s
Substitute these values into equation 3
F = 0.8×25/0.1
F = 200 N
A proton is released such that its initical velocity is from right to left across this page. THe proton's path, however, is deflected in a direction toward the bottom edge of the page due to the presence of a uniform magnetic field. What is the direction of the magnetic field
Answer:
the magnetic field is leaving the sheet
Explanation:
The magnetic force is given by the expression
F = q v x B
where bold letters indicate vectors, the modulus of this expression is
F = q v B sin θ
the direction of the force is given by the right hand rule, for a positive charge
the thumb indicates the direction of the speed, in this case from right to left
the palm the direction of the force, in our case upwards
the fingers extended the direction of the magnetic field, this case after fixing the other two components it points out of the blade
In short the magnetic field is leaving the sheet
Planet K2-116b has an Average orbital radius of 7.18x10^9 m around the star K2-116. It has a mass of about 0.257 times the mass of the earth and an orbital period of 2.7 days.
What is the orbital speed of the planet?
Determine the mass of the star.
a) v = 1.94 × 10^5 m/s
b) Ms = 2.09 × 10^24 kg
Explanation:
Given:
m = 0.257M (M = mass of earth = 5.972×10^24 kg)
= 1.535×10^24 kg
r = 7.18×10^9 m
T = 2.7 days × (24 hr/1 day) × (3600 s/1 hr)
= 2.3328×10^5 s
a) To find the orbital speed of the planet, we need to find the circumference of the planet's orbit first:
C = 2×(pi)×r
= 2(3.14)(7.18×10^9m)
= 4.51×10^10 m
The orbital speed v is then given by
v = C/T
= (4.51×10^10 m)/(2.33×10^5 s)
= 1.94 × 10^5 m/s
b) We know that centripetal force Fc is given by
Fc = mv^2/r
where v = orbital speed
r = average orbital radius
m = mass of planet
We also know that the gravitational force FG between the star K2-116 and the planet is given by
FG = GmMs/r^2
where m = mass of planet
Ms = mass of star K2-116
r. = average orbital radius
G = universal gravitational constant
= 6.67 × 10^-11 m^3/kg-s^2
Equating Fc and FG together, we get
Fc = FG
mv^2/r = GmMs/r^2
Note that m and one of the r's get cancelled out so we are left with
v^2 = GMs/r
Solving for the mass of the star Ms, we get
Ms = rv^2/G
=(7.18 × 10^9 m)(1.94 × 10^5 m/s)^2/(6.67 × 10^-11 m^3/kg-^2)
= 2.09 × 10^24 kg
(a) Calculate the height (in m) of a cliff if it takes 2.48 s for a rock to hit the ground when it is thrown straight up from the cliff with an initial velocity of 8.19 m/s. m (b) How long (in s) would it take to reach the ground if it is thrown straight down with the same speed
Answer:
(a) The height of the cliff is 9.92 m
(b) Time taken to reach the ground is 0.81 s
Explanation:
Given;
time of motion of the rock, t = 2.48 s
initial velocity of the rock, u = 8.19 m/s
(a) This is a two-way problem;
maximum upward height reached by the rock (h) + Total distance traveled downwards from the top (H).
Height of cliff = H - h
Maximum height reached by the rock;
[tex]v^2 = u^2 - 2gh\\\\0 = (8.19)^2 - (2\times 9.8)h\\\\0 = 67.08 - 19.6 h\\\\19.6h = 67.08\\\\h = \frac{67.08}{19.6} \\\\h = 3.422 \ m[/tex]
Time to reach the maximum height;
[tex]h = ut - \frac{1}{2} gt^2\\\\3.422 = 8.19t - (0.5 \times 9.8)t^2\\\\3.422 = 8.19t - 4.9t^2\\\\4.9t^2 -8.19t + 3.422 = 0\\\\This \ forms \ a quadratic \ equation ; \\\\a = 4.9, b = -8.19, c = 3.422\\\\t = \frac{-b \ \ +/- \ \ \sqrt{b^2 -4ac} }{2a} \\\\t = \frac{-(-8.19) \ \ +/- \ \ \sqrt{(-8.19)^2 -4(4.9\times 3.422)} }{2(4.9)} \\\\t = \frac{8.19 \ \ + /- \ \ \sqrt{0.0049} }{9.8} \\\\t = \frac{8.19 - 0.07}{9.8} \ \ or \ \ t = \frac{8.19 + 0.07}{9.8} \\\\t = 0.83 \ s \ \ or \ \ t = 0.84 \ s\\\\[/tex]
The time taken for rock to falll to the gound;
t₂ = 2.48 - 0.83 s
t₂ = 1.65 s
The distance traveled downwards is calculated as
H = vt + ¹/₂gt²
where;
v is the final velocity at maximum height = initial velocity when the rock starts moving downwards = 0
H = ¹/₂gt²
H = 0.5 x 9.8 x (1.65)²
H = 13.34 m
The height of the cliff = 13.34 m - 3.422m = 9.92 m
(b) time taken to reach the ground if thrown with the same speed;
h = ut + ¹/₂gt²
9.92 = 8.19t + (0.5 x 9.8)t²
9.92 = 8.19t + 4.9t²
4.9t² + 8.19t - 9.92 = 0
a = 4.9, b = 8.19, c = -9.92
use the quadratic formula;
[tex]t = \frac{-b \ \ +/- \ \ \sqrt{b^2 -4ac} }{2a} \\\\t = \frac{-8.19 \ \ +/- \ \ \sqrt{(8.19)^2 -4(4.9\times -9.92)} }{2(4.9)} \\\\t = 0.81 \ s[/tex]
what type of material is good at transferring heat?
A. A thermal insulator, such as air
B. A thermal conductor, such as water
C. A thermal insulator, such as water
D, A thermal conductor, such as air
A thermal conductor, such as water is the type of material that is good at transferring heat. Option B is correct.
What is a heat conductor?Heat conductors are substances that effectively conduct thermal energy.
The kind of substance that is effective in transferring heat is a thermal conductor, such as water.
Metals have excellent heat conductivity. Heat insulators are substances that poorly conduct thermal energy. Thermal insulators include gases like air and materials like plastic and wood.
Water conducts heat 24.17 times more quickly than air. The kind of substance that is effective in transferring heat is a thermal conductor, such as water.
Hence, option B is correct.
To learn more about the heat conductor refer;
https://brainly.com/question/12370218
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