Answer:
q = -2.19 x 10⁻⁵ C
Explanation:
Given;
mass of the particle, m = 1.5 g = 0.0015 kg
magnitude of electric field, E = 670 N/C
Electric field is given by;
[tex]E = \frac{F}{q}[/tex]
where;
q is the magnitude of the
f is the force of the charge
f = mg
[tex]E = \frac{F}{q}\\\\E = \frac{mg}{q}\\\\q = \frac{mg}{E}\\\\q = \frac{0.0015*9.8}{670} \\\\q = 2.19*10^{-5} \ C[/tex]
Since the electric field is acting downward, the force on the charge must be acting upward. Therefore, the charge must be negative
q = -2.19 x 10⁻⁵ C
Hunk travelled 540 km at an average speed of 90 km/h. If Tim completed the same amount of distance with 1 hour and 30 min less than Hunk, what was Tim's average speed for the whole journey? km/h
Answer:120
Explanation:it just is trust me
3. Consider the motion of the object whose velocity-time graph is given
in the diagram. What is the net displacement of the object between times
t = 0 and t = 2?
Velocity-time graph
8
(m/s)
8
12 16
16 m
2 m
8 m
56 m
Answer:
16 m.
Explanation:
From the question given above, we obtained the following data:
Initial velocity (u) = 0 m/s
Final velocity (v) = 8 m/s
Initial time (t1) = 0 sec
Final time (t2) = 2 secs
Net Displacement (ΔD) =?
Velocity is defined as the rate of change of the displacement of an object with time. Mathematically, it is expressed as:
Change in velocity (Δv) = change in displacement (ΔD) / change in time (Δt)
Δv = ΔD / Δt
Next we shall determine the change in velocity and time. This is illustrated below below:
Initial velocity (u) = 0 m/s
Final velocity (v) = 8 m/s
Change in velocity (Δv) =?
Change in velocity (Δv) = v – u
Change in velocity (Δv) = 8 – 0
Change in velocity (Δv) = 8 m/s
Initial time (t1) = 0 sec
Final time (t2) = 2 secs
change in time (Δt) =?
change in time (Δt) = t2 – t1
change in time (Δt) = 2 – 0
change in time (Δt) = 2 secs.
Finally, we shall determine the net displacement of the object as follow:
Change in velocity (Δv) = 8 m/s
change in time (Δt) = 2 secs.
Net Displacement (ΔD) =?
Δv = ΔD / Δt
8 = ΔD/2
Cross multiply
ΔD = 8 × 2
ΔD = 16 m
Therefore, the net displacement of the object is 16 m.
Which of the following is not a valid use of your driver's license?
proof of your ability to operate a motor vehicle
O proof of your age
O proof of your residency
proof that you have liability insurance
Answer:
Proof that you have liability insurance
Explanation:
Answer: The answer is proof that you have liability insurance
Explanation:
4. A vehicle
accelerates from
0 km/h to
100 km/h in 10 s.
What is its average
acceleration?
Answer:
Average acceleration, [tex]a=2.77\ m/s^2[/tex]
Explanation:
Given that,
Initial velocity, u = 0 km/h
Final velocity, v = 100 km/h = 27.77 m/s
Time, t = 10 s
We need to find the average acceleration of the vehicle. It is given by the change in velocity divided by time. Som,
[tex]a=\dfrac{v-u}{t}\\\\a=\dfrac{27.77-0}{10}\\\\a=2.77\ m/s^2[/tex]
So, its average acceleration is [tex]2.77\ m/s^2[/tex].
An electron with a speed of 0.95c is emitted by a supernova, where cc is the speed of light. What is the magnitude of the momentum of this electron?
Answer:
2.59×10¯²² Kgm/s
Explanation:
Data obtained from the question include:
Velocity of electron = 0.95c
Momentum =?
Next, we shall determine the velocity of the electron. This can be obtained as follow:
Velocity of electron = 0.95c
Velocity of Light (c) = 3×10⁸ m/s
Velocity of electron = 0.95c
Velocity of electron = 0.95 × 3×10⁸
Velocity of electron = 2.85×10⁸ m/s
Finally, we shall determine the mometum of the electron.
Momentum is simply defined as the product of mass and velocity. Mathematically, it is expressed as:
Momentum = mass x Velocity
Thus, with the above formula, we calculate the momentum of the electron as follow:
Mass of electron = 9.1×10¯³¹ Kg
Velocity of electron = 2.85×10⁸ m/s
Momentum of electron =?
Momentum = mass x Velocity
Momentum = 9.1×10¯³¹ × 2.85×10⁸
Momentum = 2.59×10¯²² Kgm/s
Therefore, the momentum of the electron is 2.59×10¯²² Kgm/s
Explain why a Merry-Go-Round and a Ferris Wheel have a constant acceleration when they are moving?
Answer:
merry go round and Ferris wheel have a constant acceleration due to the change in direction at every point.
Answer:
A merry-go-round is accelerating. Acceleration is a change in speed, direction, or both. Even though the speed of the merry-go-round does not change, its direction constantly changes as it spins.
Explanation:
A commuter backs her car out of her garage with an acceleration of 1.40 m/s2.A) How long does it take her to reach a speed of 2.00 m/s?B) If she then breaks to a stop in 0.800 s, what is her deceleration?
Answer:
(A) 1.43secs
(B) -2.50m/s^2
Explanation:
A commuter backs her car out of her garage with an acceleration of 1.40m/s^2
(A) When the speed is 2.00m/s then, the time can be calculated as follows
t= Vf-Vo/a
The values given are a= 1.40m/s^2 , Vf= 2.00m/s, Vo= 0
= 2.00-0/1.40
= 2.00/1.40
= 1.43secs
(B) The deceleration when the time is 0.800secs can be calculated as follows
a= Vf-Vo/t
= 0-2.00/0.800
= -2.00/0.800
= -2.50m/s^2
A satellite dish has the shape of a parabola when viewed from the side. The dish is inches wide and inches deep. How far is the receiver from the bottom of the dish if the receiver is placed at the focus
Complete question is;
A satellite dish has the shape of a parabola when viewed from the side. The dish is 60 inches wide and 45 inches deep. How far is the receiver from the bottom of the dish if the receiver is placed at the focus?
Answer:
the receiver should be put 40 inches from the bottom of the dish on the concave side of the dish
Explanation:
The base of the dish would simply be the vertex of parabola.
Since we want to find how far the receiver is from the bottom, the place where we'll place the receiver is simply the focus of the parabola.
Now, for example, if this is a parabola that opens upward and has it's vertex at the origin, then half of the diameter at a height of 45 inches gives the two points (60, 22.5) and (-60, 22.5)
Standard form equation of parabola with vertex at origin and pointing upwards is given by;
x² = 4ay
Plugging in the values of x and y gives;
60² = 4a(22.5)
3600/90 = a
a = 40 inches
Thus, the receiver should be put 40 inches from the vertex on the concave side of the dish
it is easier to swim in Ocean than in a water
Answer:
Explanation:
Ocean contains salty water which causes the object to float rather than sinking, So yes it's easy to swim in ocean than water without salt.
A Lotus will travel 275 meters in 4.71 seconds. What is this car's average speed?
A ski lift has a one-way length of 1 km and a vertical rise of 200 m. The chairs are spaced 20 m apart, and each chair can seat three people. The lift is operating at a steady speed of 10 km/h. Neglecting friction and air drag, and assuming that the average mass of each loaded chair is 250 kg, determine the power required to operate this ski lift. Also, estimate the power required to accelerate this ski lift in 17 s to its operating speed when it is first turned on.
Answer:
Explanation:
The question states that the chairs are spaced 20 m apart through a length of 1 km, or say, 1000 m.
It also does say that each chair weighs 250 kg, and as such the load is
M = 50 * 250
M = 12500.
Taking into consideration, the initial and final heights, we have
h1 = 0, h2 = 200 m
The work needed to raise the chairs,
W = mgh, where h = h2 - h1
W = 12500 * 9.81 * (200 - 0)
W = 2.54*10^7 J
The work is done at a rate of 10 km/h, and at a distance of 1 km, time taken would be
t = 1/10 = 0.1 h or say, 360 s
The power needed thus, is
P = W/t
P = 2.54*10^7 / 360
P = 68125 W, or 68 kW
Initial velocity, u = 0 m/s
Final velocity, v = 10 km/h = 2.78 m/s
Startup time, t is 17 s
Acceleration during the startup then is
a = (v - u)/t
a = 2.78/17
a = 0.163 m/s²
The power needed for the acceleration is
P = ½m [(v² - u²)/t]
P = ½ * 12500 * [2.78²/17]
P = 6250 * 0.455
P = 2844 W
The average gorilla can travel 40.23 meters in 4 seconds, calculate the average speed in meters per second (m/s) 
Answer:
10.0575 m/s
Explanation:
40.23 divide by 4
Answer:
it is 10.0575 m/s
Explanation:
The average speed is calculated by total distance/total time taken. Here, the distance is 40.23 meters and time is 4 seconds.
So, average speed = 40.23/4 m/s
= 10.0575 m/s
The energy radiated per unit surface area (across all wavelengths) for a black body with temperature 2200. Use 5.67 x 10-8 for the Stefan-Boltzmann constant.The ____________ describes the power radiated from a black body in terms of its temperature. Specifically, the total energy radiated per unit surface area of a black body across all wavelengths per unit time is proportional to the fourth power of the black body's thermodynamic temperature
Answer:
Stefan-Boltzmann Law describes the power radiated from a black body in terms of its temperature. Specifically, the total energy radiated per unit surface area of a black body across all wavelengths per unit time is proportional to the fourth power of the black body's thermodynamic temperature
Explanation:
So we now know that
energy per unit area is = zigma x T^4
From this
T = temperature in kelvin
zigma is stefan boltzman constant
So
E/A = 5.67 x 10^-8 x (2200)⁴
= 1.33x 10^6 W/m^2
please help! find magnitude and direction (the counterclockwise angle with the +x axis) of a vector that is equal to a + c
Answer:
Option (2)
Explanation:
From the figure attached,
Horizontal component, [tex]A_x=A\text{Sin}37[/tex]
[tex]A_x=12[\text{Sin}(37)][/tex]
= 7.22 m
Vertical component, [tex]A_y=A[\text{Cos}(37)][/tex]
= 9.58 m
Similarly, Horizontal component of vector C,
[tex]C_x[/tex] = C[Cos(60)]
= 6[Cos(60)]
= [tex]\frac{6}{2}[/tex]
= 3 m
[tex]C_y=6[\text{Sin}(60)][/tex]
= 5.20 m
Resultant Horizontal component of the vectors A + C,
[tex]R_x=7.22-3=4.22[/tex] m
[tex]R_y=9.58-5.20[/tex] = 4.38 m
Now magnitude of the resultant will be,
From ΔOBC,
[tex]R=\sqrt{(R_x)^{2}+(R_y)^2}[/tex]
= [tex]\sqrt{(4.22)^2+(4.38)^2}[/tex]
= [tex]\sqrt{17.81+19.18}[/tex]
= 6.1 m
Direction of the resultant will be towards vector A.
tan(∠COB) = [tex]\frac{\text{CB}}{\text{OB}}[/tex]
= [tex]\frac{R_y}{R_x}[/tex]
= [tex]\frac{4.38}{4.22}[/tex]
m∠COB = [tex]\text{tan}^{-1}(1.04)[/tex]
= 46°
Therefore, magnitude of the resultant vector will be 6.1 m and direction will be 46°.
Option (2) will be the answer.
A wildebeest runs with an average speed of 4.0\,\dfrac{\text m}{\text s}4.0 s m 4, point, 0, start fraction, start text, m, end text, divided by, start text, s, end text, end fraction for 15\,\text s15s15, start text, s, end text. What was its distance travelled in meters?
Answer:
60m
Explanation:
Answer: 60
Explanation: I got it right on Khan
A -5.40nC point charge is on the x axis at x = 1.25m . A second point charge Q is on the x axis at -0.625m.
A) What must be the charge Q for the resultant electric field at the origin to be 50.0N/C in the +x direction?
B) What must be the charge Q for the resultant electric field at the origin to be 50.0N/C in the -x direction?
Answe
a) Q = 0.820 10⁻⁹ C , b) Q = -3.52 10⁻⁹ C
Explanation:
The electric field is given by the formula
E = k q / r²
where E is a vector quantity, so it must be added as a vector
E_total = E₁ + E₂
let's look for the two electric fields
E₁ = k q₁ / r₁²
E₁ = 9 10⁹ 5.4 10⁻⁹ / 1.25²
E₁ = 31.10 N / C
E2 = k Q / r₂²
E2 = 9 10⁹ Q / 0.625²
E2 = 23.04 10⁹ Q N / C (1)
now we can solve the two cases presented
a) The total field is
E_total = 50.0 N / C towards + x
since the test charge is positive the electric field E1 points to the right in the direction of the + x axis, so the equation is
E_total = E1 + E₂
E₂ = E_toal - E₁
E₂ = 50.0 -31.10
E2 = 18.9 N /C
With the value of the electric field we can calculate the charge (Q) using equation 1
E₂ = 23.04 10⁹ Q
Q = E₂ / 23.04 10⁹
Q = 18.9 / 23.04 10⁹
Q = 0.820 10⁻⁹ C
the charge on Q is positive
b) E_total = -50.0 N / C
E_total = E₁ + E₂
E₂ = E_total - E₁
E2 = -50.0 - 31.10
E2 = -81.10 N /C
we calculate the charge
Q = E2 / 23.04 10⁹
Q = -81.1 / 23.04 10⁹
Q = -3.52 10⁻⁹ C
for this case the charge is negative
An 85 kg skydiver is falling through the air at a constant speed of 195 km h-1. At what rate does air resistance remove energy from the skydiver?
Answer:
46041J
Explanation:
Using Energy lost= mgh
Changing to standard its we have
= 195*1000/3600=54.2m/s
So = 85*54.2*10= 46041J
Answer:
45167.15 J/s
Explanation:
mass of the man = 85 kg
The man's speed = 195 km/h = 195 x 1000/3600 = 54.167 m/s
The man's weight = mg
where
m is the mass
g is acceleration due to gravity = 9.81 m/s^2
weight = 85 x 9.81 = 833.85 N
The rate at which energy is removed from the man = speed x weight
==> 54.167 x 833.85 = 45167.15 J/s
A runner jumps off the ground at a speed of 16m/s. At what angle did he jump from the ground if he landed 8m away?
Answer:lol I don’t know good qeustion
Explanation:
Which of these terms is defined as the ability to cause motion or create change? A. efficiency B. energy C. force D. sound
The term that defines the ability to cause motion or create change is called force. Details about force can be found below.
What is force?Force is the physical quantity that denotes ability to push, pull, twist or accelerate a body and which has a direction.
Force is measured in Newtons and can be calculated by multiplying the mass of the body by its acceleration.
Therefore, it can be said that the term that defines the ability to cause motion or create change is called force.
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what is the speed of a truck that travels 10 km in 10 minutes?
Answer:
10 minutes: 10 km
1 minute: 10 ÷ 10 = 1 km
the speed of the truck is 1km/min
Answer:
1 kilometer/minute
Explanation:
If we want to find the speed, we must divide the distance by the time.
[tex]s= \frac {s}{t}[/tex]
The truck travels a distance of 10 kilometers in 10 minutes.
[tex]d= 10 km\\t=10 min[/tex]
Substitute the values into the formula and divide.
[tex]s=\frac{d}{t}[/tex]
[tex]s=\frac{10 km}{10min}[/tex]
[tex]s= 1 km/min[/tex]
The speed of the truck is 1 kilometer per minute.
The speed of a bus increases uniformly from
15 ms- to 60 ms in 20 seconds. Calculate
a. the average speed,
b. the acceleration,
C. the distance travelled during the entire
period The speed of a bus increases uniformly from
15 ms- to 60 ms in 20 seconds. Calculate
a. the average speed,
b. the acceleration,
C. the distance travelled during the entire
period
Explanation:
a. For constant acceleration:
v_avg = ½ (v + v₀)
v_avg = ½ (60 m/s + 15 m/s)
v_avg = 37.5 m/s
b. a = (v − v₀) / t
a = (60 m/s − 15 m/s) / 20 s
a = 2.25 m/s²
c. x = v_avg t
x = (37.5 m/s) (20 s)
x = 750 m
A paper airplane is thrown horizontally with a velocity of 20 mph. The plane is in the air for 7.63 s before coming to a standstill on the ground. What is the acceleration of the plane?
Answer:
-1.17 m/s²
Explanation:
Given:
v₀ = 20 mph = 8.94 m/s
v = 0 m/s
t = 7.63 s
Find: a
v = at + v₀
0 m/s = a (7.63 s) + 8.94 m/s
a = -1.17 m/s²
The acceleration of the plane will be:
"-1.17 m/s²".
Acceleration and VelocityAccording to the question,
Velocity, v₀ = 20 mph or,
= 8.94 m/s
and,
v = 0 m/s
Time, t = 7.63 s
We know the relation,
→ v = at + v₀
By substituting the values,
0 = a × 7.63 + 8.94
7.63a = - 8.94
a = -[tex]\frac{8.94}{7.63}[/tex]
= - 1.17 m/s²
Thus the response above is correct.
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Public television station KQED in San Francisco broadcasts a sinusoidal radio signal at a power of 777 kW. Assume that the wave spreads out uniformly into a hemisphere above the ground. At a home 5.00 km away from the antenna,
(a) what average pressure does this wave exert on a totally reflecting surface,
(b) what are the amplitudes of the electric and magnetic fields of the wave, and
(c) what is the average density of the energy this wave carries?
(d) For the energy density in part (c), what percentage is due to the electric field and what percentage is due to the magnetic field?
Answer:
A) P = 3.3 × 10^(-11) Pa
B) Amplitude of electric field = 1.931 N/C
Amplitude of magnetic field = 6.44 × 10^(-9) T
C) μ_av = 1.65 × 10^(-11) J/m³
D) 50% each for the electric and magnetic field
Explanation:
A) First of all let's calculate intensity.
I = P_av/A
We are given;
P_av = 777 KW = 777,000 W
Distance = 5 km = 5000 m
Thus;
I = 777000/(2π × 5000²)
I = 0.00495 W/m²
Now, the average pressure would be given by the formula;
P = 2I/C
Where C is speed of light = 3 × 10^(8) m/s
P = (2 × 0.00495)/(3 × 10^(8))
P = 3.3 × 10^(-11) Pa
B) Formula for the amplitude of the electric field is gotten from;
E_max = √[2I/(εo•c)].
Where εo is the Permittivity of free space with a constant value of 8.85 × 10^(−12) c²/N.mm²
I and c remain as before.
Thus;
E_max = √[(2 × 0.00495)/(8.85 × 10^(−12) × 3 × 10^(8))]
E_max = √3.72881355932
E_max = 1.931 N/C
Formula for amplitude of magnetic field is gotten from;
B_max = E_max/c
B_max = 1.931/(3 × 10^(8))
B_max = 6.44 × 10^(-9) T
C) Formula for average density is;
μ_av = εo(E_rms)²
Now, E_rms = E_max/√2
Thus;
E_rms = 1.931/√2
μ_av = 8.85 × 10^(−12) × (1.931/√2)²
μ_av = 1.65 × 10^(-11) J/m³
D) The energy density for the electric and magnetic field is the same. So both of them will have 50% of the energy density.
A certain common-emitter amplifier has a voltage gain of 100. If the emitter bypass capacitor is removed:___________.
a. The circuit will become unstable b. The voltage gain will decrease
c. The voltage gain will increase d. The circuit will become stable
Answer:
b the voltage gain will decrease
Explanation:
Q=CV
which water molecules have the greatest kinetic energy
A ball of mass m moving with speed V collides with another ball of mass 2m (e= 1/2) in a horizontal smooth fixed circular tube of radius R (R is sufficiently large R>>>d). The time after which next collision will take place is:________
Answer:
[tex]$ \frac{4\pi R}{V}$[/tex]
Explanation:
Given :
Mass of ball 1 = m
Mass of ball 2 = 2m
Since, R>>>d, the collision is head on.
Therefore, we get
[tex]$ \frac{v_1 -v_2}{V}=\frac{1}{2}$[/tex]
[tex]$ \therefore \frac{\text{velocity of seperation}}{\text{velocity of approach}}= v_1-v_2 = \frac{V}{2}$[/tex]
Relative velocity is given by V/2. So, we get the time when the masses will again collide as
[tex]$ t = \frac{2\pi R}{\frac{V}{2}}=\frac{4\pi R}{V} $[/tex]
What is the Creation Mandate?
An elevator moves downward in a tall building at a constant speed of 5.05 m/s. Exactly 5.75 s after the top of the elevator car passes a bolt loosely attached to the wall of the elevator shaft, the bolt falls from rest.
(a) At what time does the bolt hit the top of the still-descending elevator? (Assume the bolt is dropped at t = 0 s.)
(b) Estimate the highest floor from which the bolt can fall if the elevator reaches the ground floor before the bolt hits the top of the elevator. (Assume 1 floor ≌ 3 m.)
Answer:
Explanation:
The elevator is moving with uniform speed and bolt will fall with acceleration due to gravity g .
Displacement of elevator when bolt starts falling
= 5.05 x 5.75 = 29 m
Let after time t bolt reaches the elevator
in time t , displacement of bolt = 1/2 g t²
= .5 x 9.8 x t² = 4.9 t²
displacement of elevator = 5.05 t
position of elevator = 29 + 5.05 t
According to question ,
29 + 5.05 t = 4.9 t²
4.9 t² - 5.05 t - 29 = 0
t = 3 s approx .
b )
Distance covered by the bolt
= 1 /2 g t²
= .5 x 9.8 x 9
= 44.1 m
Bolt must have to fall from a height of 44.1 m
or in terms of floor it is
44.1 / 3 = 15 th floor .
A car stops in 120 m. If it has an acceleration of –5m/s 2 , how long did it take to stop
Answer:
t=240s
Explanation:
Distance=120m
Acceleration=-5m/s^2
v=0
Let u=x m/s
Using equation v^2-u^2=2as:-
0-x=2(-5)(120)
-x=-1200
x=1200m/s
Using now equation v=u+at:-
0=1200+-5t
5t=1200
t=240s
If a car stops at 120 meters. If it has an acceleration of –5 meters/second², then it would take 6.928 seconds to stop.
What is acceleration?The rate of change of the velocity with respect to time is known as the acceleration of the object.
As given in the problem a car stops at 120 meters. If it has an acceleration of –5 meters/second², then we have to find out how long it would take seconds to stop.
By using the second equation of motion,
s = ut + 1/2at²
The distance traveled by car before stopping = 120 meters
acceleration = –5 meters/second²
-120 = 0 + 0.5×( –5)t²
t² = 120/2.5
t² =48
t = 6.928 seconds
Thus, the time taken by the car before stopping would be 6.928 seconds.
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Gwen releases a rock at rest from the top of a 40-m tower. If g = 9.8 m/s2 and air resistance is negligible, what is the speed of the rock as it hits the ground?
Answer:
[tex]28\; \rm m \cdot s^{-1}[/tex].
Explanation:
Short ExplanationApply the SUVAT equation [tex]\left(v^2 - u^2) = 2\, a \, x[/tex], where:
[tex]v[/tex] is the final velocity of the object,[tex]u[/tex] is the initial velocity of the object, [tex]a[/tex] is the acceleration (should be constant,) and[tex]x[/tex] is the displacement of the object while its velocity changed from [tex]v[/tex] to [tex]u[/tex].Assume that going downwards corresponds to a positive displacement. For this question:
[tex]v[/tex] needs to be found.[tex]u = 0[/tex] because the rock is released from rest.[tex]a = g = 9.8 \; \rm m\cdot s^{-2}[/tex].[tex]x = 40\; \rm m[/tex].Solve this equation for [tex]v[/tex]:
[tex]\displaystyle v = \sqrt{2\, a\, x + u^2} = \sqrt{2\times 9.8 \times 40} = 28\; \rm m \cdot s^{-1}[/tex].
In other words, the rock reached a velocity of [tex]28\; \rm m\cdot s^{-1}[/tex] (downwards) right before it hits the ground.
ExplanationLet [tex]v[/tex] be the velocity (in [tex]\rm m \cdot s^{-1}[/tex]) of this rock right before it hits the ground. Under the assumptions of this question, it would take a time of [tex]t = (v / 9.8)[/tex] seconds for this rock to reach that velocity if it started from rest and accelerated at [tex]9.8\; \rm m \cdot s^{-2}[/tex].
Note that under these assumptions, the acceleration of this rock is constant. Therefore, the average velocity of this rock would be exactly one-half the sum of the initial and final velocity. In other words, if [tex]u[/tex] denotes the initial velocity of this rock, the average velocity of this rock during the fall would be:
[tex]\displaystyle \frac{u + v}{2}[/tex].
On the other hand, [tex]u = 0[/tex] because this stone is released from rest. Therefore, the average velocity of this rock during the fall would be exactly [tex](v / 2)[/tex].
The displacement of an object over a period of time is equal to the length of that period times the average velocity over that period. For this rock, the length of this fall would be [tex]t = (v / 9.8)[/tex], while the average velocity over that period would be [tex](v / 2)[/tex]. Therefore, the displacement (in meters) of the rock during the entire fall would be:
[tex]\displaystyle \left(\frac{v}{2}\right) \cdot \left(\frac{v}{9.8}\right) = \frac{v^2}{19.6}[/tex].
That displacement should be equal to the change in the height of the rock, [tex]40\; \rm m[/tex]:
[tex]\displaystyle \frac{v^2}{19.6} = 40[/tex].
Solve for [tex]v[/tex]:
[tex]v = 28\; \rm m \cdot s^{-1}[/tex].
Once again, the speed of the rock would be [tex]28\;\rm m \cdot s^{-1}[/tex] right before it hits the ground.