A particle of mass m is fired upwards from the surface of a planet of mass M
and radius R with velocity
Show that the maximum height the particle attains is R/3.

Answers

Answer 1

At the maximum height the particles position has been shown as [tex]\frac{R}{3}[/tex].

The given parameters;

mass of the particle, = Mradius of the particle, = Rmaximum height the particle attains = R/3

The velocity of the particle is given as;

[tex]v^2 = \frac{GM}{2R}[/tex]

The total mechanical energy of the particle is given as;

[tex]-\frac{GMm}{R} + \frac{1}{2} mv^2 = - \frac{GMm}{R} + \frac{1}{2} mv^2[/tex]

At maximum height the final velocity of the particle is zero.

[tex]-\frac{GMm}{R} + \frac{1}{2} mv^2 = - \frac{GMm}{R +h}[/tex]

[tex]-\frac{GMm}{R} + \frac{1}{2} m\times \frac{GM}{2R} = - \frac{GMm}{R +h}\\\\-\frac{GMm}{R} + \frac{GMm}{4R} = - \frac{GMm}{R +h}\\\\- \frac{3GMm}{4R} = - \frac{GMm}{R +h}\\\\- \frac{3}{4R} = - \frac{1}{R+ h} \\\\3(R+ h) = 4R\\\\3R + 3h = 4R\\\\3h = 4R - 3R\\\\3h = R\\\\h = \frac{R}{3}[/tex]

Thus, at the maximum height the particles position has been shown as [tex]\frac{R}{3}[/tex].

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Related Questions

Physical activities teaches an individual sense of responsibility and initiative.
True Or False

Answers

Answer:

true

Explanation:

Physical fitness is a personal responsibility so I would say true

the correct answer is true :)

Is snowflakes forming in a cloud a chemical or physical change

Answers

Answer:

Physical change.

A snowflake is still considered water whether its liquid or solid.

Answer:

mark me as brainliest !! PHYSICAL CHANGE

Explanation:

A snowflake is composed of ice, which is water in the solid phase. Water is a chemical compound of oxygen and hydrogen atoms.

You are observing a star that is 250 million light years away. From the starlight you are observing now, the appears to be 30 million years old and you determine that the star has a lifetime of 120 million years. How long will it be until Earth receives light from the supernova that occurs at the end of the life of the star

Answers

What ever games your playing it wont work you cant defeat me hahhahha oh I know :O but he can AHHHH :D D: NOOOO IMPOSSIBLE.

A box is pushed horizontally with constant speed across a rough horizontal surface. Which of the following must be true?
a) The friction is less than the applied force
b) There is no friction acting on the box
c) The friction is greater than the applied force
d) The friction is equal to the applied force

Answers

D

Because if an object is moving at a constant speed the force of friction must equal the applied (horizontal) force, and for it to be accelerating or decelerating, the force of friction and the applied force must be unequal

relationship between the length (l) and ohmic conductor, its thickness (d) and the opposition (R) it offers a current passage​

Answers

Answer:

Ohm’s Law states that current is proportional to voltage; circuits are ohmic if they obey the relation V=IR.

Explanation:

LEARNING OBJECTIVES

Contrast shape of current-voltage plots for ohmic and non-ohmic circuits

Un péndulo de 4 m de longitud tiene una frecuencia de 5Hz. Calcular la longitud de otro péndulo que en el mismo lugar tiene una frecuencia de 4Hz

Answers

Conociendo la longitud y frecuencia de un péndulo, queremos encontrar la longitud de otro pendulo de tal forma que tenga otra frecuencia.

Veremos que la longitud del nuevo péndulo debe ser 6.25m

Sabemos que un péndulo de 4m de longitud tiene una frecuencia de 5Hz.

La frecuencia de un péndulo está dada por:

[tex]f = \frac{1}{2*\pi} *\frac{g}{l}[/tex]

Donde g es la aceleración gravitatoria y l es la longitud del péndulo, remplazando los datos que tenemos en esa ecuación obtenemos:

[tex]5 Hz = \frac{1}{2*3.14} *\sqrt{\frac{g}{4m} } \\\\(5Hz*2*3.14)^2*4m = g = 3,943.8 m/s^2[/tex]

Ahora debemos encontra la longitud de tal forma que la frecuencia sea 4Hz, entonces debemos resolver:

[tex]4Hz = \frac{1}{2*3.14} *\sqrt{ \frac{3943.8m/s^2}{l} }\\\\4hz*2*3.14 = \sqrt{ \frac{3943.8m/s^2}{l} }\\\\l =\frac{3943.8m/s^2}{ (4hz*2*3.14)^2} = 6.25m[/tex]

La longitud del nuevo péndulo deve ser 6.25m

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1.protozoo ore ?
A. multicellular organisms B. one - Celled animals
C. amembers of the group Protocista
D. unicellulor Plants​

Answers

Answer:

c

Explanation:

amembers of the group protocista

8. What is the kinetic Energy of the 75 kg skydiver if she is falling at 52 m/s?
Formula:
Variables with units:
Work with Units:
Final Answer with Units:

Answers

Answer:

101,400 J

Explanation:

The kinetic energy of an object can be found by using the formula

[tex]k = \frac{1}{2} m {v}^{2} \\ [/tex]

m is the mass

v is the velocity

From the question

m = 75 kg

v = 52 m/s

We have

[tex]k = \frac{1}{2} \times 75 \times {52}^{2} \\ = \frac{1}{2} \times 75 \times 2704 \\ = 75 \times 1352 \\ = 101400[/tex]

We have the final answer as

101,400 J

Hope this helps you

a father pulls his young daughter on a sled (where the combined mass of his daughter and the sled are 40 kg) with a constant velocity up a snowy hill that is inclined at 14 to the horizontal. a) if the coefficient of kinetic friction between the sled's runners and the snow is 0.15, what is the tension force of the rope on which the father pulls

Answers

Answer:

Explanation:

We are not told what angle the pull rope is to any other reference. That could make a huge difference in the result.

If we ASSUME that the rope pulls parallel to the slope

Then , if T is rope tension

                                  F = ma

T - mgsinθ - μmgcosθ = m(0)

                                 T = mg(sinθ + μcosθ)

                                 T = 40(9.8)(sin14 + 0.15cos14)

                                 T = 151.88677... 150 N

If the rope pulls the sled at a positive angle relative to the slope, As one might expect from an adult holding the rope, then the tension will be increased because only the Tension portion parallel to the slope causes motion in that direction, but will be decreased because the Normal force, and therefore the friction force, of the slope on the sled will be decreased.

A boy 11.0 m above the ground in a tree throws a ball for his dog, who is standing right below the tree and starts running the instant the ball is thrown. If the boy throws the ball upward at 50.0 ∘ above the horizontal, at 8.00 m/s .
How fast must the dog run to catch the ball just as it reaches the ground?
How far from the tree will the dog catch the ball?

Answers

12414253

Explanation:

What process makes this pattern on the ocean floor?

Answers

Plate tectonics


and the ocean floor
Bathymetry, the shape of the ocean floor, is largely a result of a process called plate tectonics.

please give me brainliest

Why potential energy is remian constant when solid body is heated?

Answers

the temperature remains constant because the given heat is used to increase only the potential energy of the molecules of the given substance (which results in the change of its state) and not the kinetic energy as temperature of a body is actually the measure of the average kinetic energy of its molecules.

Which is the largest number? O A. 9.9 x 106 O B. 4.5 x 107 O c. 5.5 x 105 O D. 5.8 x 108​

Answers

Answer:

107

Explanation:

It's the biggest number

CAN SOMEBODY PLEASE HELP ME?!?!?!??!??!?!?!?!

Answers

Answer:

B. The force of gravity that acts on the kitten

Explanation:

Water which contains large amounts of calcium dissolved within it results from
a) factory sewage outfalls.
b) water dissolving materials in the ground.
c) volcanic activity.
d) increase in number of wells in area.

Answers

Answer: B

Explanation:

The other options have nothing to do with the water apart from transporting it.

What force causes the passengers in a car to move forward when the car comes to a sudden stop?

Answers

Answer:

You and the car have inertia. If the car comes to a sudden stop, your body tends to keep moving forward. When the car starts moving again, your body tends to stay at rest. You move forward because the car seat exerts an unbalanced force on your body.

Explanation:

This is due to inertia. When the speeding bus stops suddenly, lower part of the body comes to rest while the upper part of the body tends to maintain uniform motion. Hence, the passenger's are thrown forward.

A football is kicked with a velocity of 5 m/s at an angle of 53° above the horizontal. What is its speed at the
maximum height?
A) 3 m/s
B) 6 m/s
C) 9 m/s
D) 12 m/s
E) 15 m/s

Answers

A is the correct answer

A mini car of mass 750kg has a head on collision with suv of mass 1200kg traveling at 40m/s.Both cars stop dead.How fast was the mini car traveling

Answers

Answer:

Explanation:

Conservation of momentum

Final momentum is zero

1200(40) + 750v = (1200 + 750)(0)

v = - 1200(40)/750

v = - 64 m/s

The negative sign means the mini car was traveling in the opposite direction of the SUV

2. A 6.0 kg mass is pulled along a horizontal surface where the coefficient of friction is 0.20.
a) What is the friction force acting on the mass?
b) What force is needed to accelerate it at 0.68 m/s^(2)?

Answers

Answer:

Below

Explanation:

a) To find the force of friction acting on the mass we can use this formula :

     friction = coefficientoffriction x normal force

First we need to find the normal force of this object :

     Fn = mg

          = (6.0)(9.8)

          = 58.8 N

Now we can find the force of friction acting on the object :

     friction = (0.20)(58.8N)

                 = 11.76 N

                 = 12 N (we round this to 2 sig figs)

b) To find the force needed to accelerate this object at 0.68 m/s^2 use this :

     F = ma

     0.68 = x - 11.76 / 6

     x = 15.84

     x = 16 N

Hope this helps! Best of luck <3

Lab: Motion with Constant Acceleration Assignment: Lab Report

Write your lab report


Someone please help me do this, ill give brainliest

Answers

Answer:

Table C:

Fan Speed Observations of Position vs. Time Graphs

Low:

The slope is curved and it increases as you go up . The points start off close but they spread out as the time increases.

Medium:

The speed increases quicker than the graph for low speed. The graph is less curved than the one for low speed. Also, the points spread out faster than they did for low speed as the time increases.

High:

The Graph has a smaller curve then the low and medium speed. Also, the points are the furthest apart. The slope is not as spaced out as it was for the rest of the speed graphs.

Explanation:

hope it helps

Variations in the angle of inclination or the mass of the cart could be investigated further to investigate the impact on acceleration and further validate the principles of constant acceleration motion.

Objective: The goal of this lab experiment was to investigate the motion of an item with constant acceleration and to examine its velocity as a function of time.

Materials:

Smooth, inclined plane

Cart or tiny wheeled object

Stopwatches and timers

Measuring tape or meterstick

Procedure:

Set up the inclined plane at a 45-degree angle () to the horizontal surface. Check that the plane is smooth and clear of obstacles.

Place the cart or small wheeled object at the bottom of the inclined plane.

Using a meterstick or measuring tape, determine the height (h) and length (L) of the inclined plane.

Ascertain that the cart is at rest at the starting point, which is located at the bottom of the inclined plane.

As soon as the cart is freed and begins to move, start the stopwatch or timer.

Calculate the time (t) it takes the cart to reach each place along the inclined plane. To ensure reliable data gathering, repeat the experiment numerous times.

Determine the time intervals (Δt) between each position for velocity analysis

Data:

Position (m) Time (s) Time Interval (Δt) (s)

0.0                   0.00           -

0.5                   0.50        0.50

1.0                   0.75        0.25

1.5                    1.10              0.35

2.0                    1.50        0.40

Analysis:

Calculate the average velocity between each position by dividing the position change by the time interval (x/t).

Create a graph that plots average velocity (V_avg) versus time (t).

Results:

A straight line emerges from the graph of average velocity against time, demonstrating that the cart's motion was subject to continuous acceleration along the inclined plane. The slope of the graph reflects the acceleration (a) of the cart.

Conclusion:

The experiment successfully demonstrated motion along an inclined plane with constant acceleration. The graph of average velocity vs time revealed important information about the cart's speed, with a linear relationship suggesting steady acceleration. This experiment emphasizes kinematic principles and the significance of using velocity-time data to understand the motion of objects under constant acceleration.

Hence, variations in the angle of inclination or the mass of the cart could be investigated further to investigate the impact on acceleration and further validate the principles of constant acceleration motion.

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Energy Transfer and Temperature Quick Check 1 of 41 of 4 Items Question Use the table to answer the question. Sample Observation 1 The drop of food coloring spreads slowly. 2 The drop of food coloring spreads very quickly. A student places a drop of food coloring into two water samples. Her observations are shown in the table. Which statement best explains the observations in the table? (1 point) The water molecules of sample 1 are moving faster. The water molecules of sample 1 are moving faster. The temperature of sample 2 is close to freezing. The temperature of sample 2 is close to freezing. The temperature of sample 2 is higher. The temperature of sample 2 is higher. The water molecules of sample 1 are transferring more kinetic energy. The water molecules of sample 1 are transferring more kinetic energy.

Answers

Answer: Measure the initial temperature of the water using the thermometer Poke through a food substance measuring 0.5 grams using the needle with the handle. Turn on fire on the burner. Set the food substance on the needle to fire on the burner. Once the food substance starts to burn, place it under the test tube so the water inside it can absorb heat.

Explanation:

Hope this helps!

A machine whose efficiency is 75% is used to lift a load of 100m.calculate the effort put into the machine if it has a velocity ratio of 4.

Answers

Explanation:

M.A = load / Effort

efficiency = M.A/V.R X 100

75 = M.A / 4 X 100

75 = 25 X M.A

M.A = 75/25 = 3

M.A = load / effort

3 = 100/E

E = 100/3 = 33.333

A machine whose efficiency is 75% is used to lift a load of 100m. the effort needed to put into the machine is 33.33 meters if the velocity ratio is 4.

What is the mechanical advantage?

Mechanical advantage is defined as a measure of the ratio of output force to input force in a system, It is used to analyze the forces in simple machines like levers and pulleys.

Mechanical advantage = output force(load) /input force (effort)

Simple machines like static pulleys, as well as a movable pulleys, provide a great amount of mechanical advantage.

A machine whose efficiency is 75% is used to lift a load of 100m.calc if it has a velocity ratio of 4.

As we know that the mechanical advantage of a machine is equal to the product of its efficiency and velocity ratio.

mechanical advantage  = velocity ratio   ×Efficiency

       =4 × 0.75

       = 3

The mechanical advantage is 3 , which means the ratio of load to effort is 3

load / effort = 3

100 m/effort =3

effort = 33.33 m

Thus, the effort put into the machine comes out to be 33.33 m.

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PLEASE ANSWER ASAP IM GONNA MARK AS BRAINLIEST

What is the value of the force measured by the spring balance? ​

Answers

Spring balance is a mechanical device used for measuring the weight or force of an object by opposing the force of gravity with the force of an extended spring. The principle behind its working is the principle of Hooke's law.

Bài 1. Một vật được đặt trên một mặt phẳng nghiêng hợp với mặt phẳng nằm ngang một góc  = 300.

Answers

Answer:

3q

Explanation:

A__________ shows how velocity changes over time

Answers

Velocity time graph goes into the blank hope it helps please mark me brainliest

How 2cos theta ×sin theta is =sin2theta

Answers

Answer:

Can you rewrite that sorry

Explanation:

What happens to the size of an Object when it is heated ?​

Answers

Answer:

size get smaller maybe there is no object remaining

Answer:

If they are heated the size. will be decreased.

Technician a says that the piston engine starts and stops several times per 2nd technician B says that with the rotary engine each rotor has 3 working chambers so it acts like a 3 cylinder engine while it is at operating

Answers

Answer:

Explanation:

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When converted to a household measurement, 9 kilograms is approximately equal to a

Answers

Answer:

D) 19.8 lbs

Explanation:

1kg in household measurement is equal to 35.274 ounces. 35.274*9=317.466 ounces.

1kg is also equal to 2.205 lbs. 9*2.205=19.8416

9 kg is also equal to 9000 grams, but grams are not a part of the household measurement system

a) 9000 grams. b) 9000 ounces. c) 19.8 ounces. d) 19.8 pounds.

This leaves us with 19.8 lbs

What is the intensity level for a sound of Intensity 10-⁶w/m²​

Answers

Thus, the intensity of the sound level is 63.01 dB.
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