Answer:
[tex]a=0.2*10^{-5}g[/tex]
Explanation:
From the question we are told that:
Mass [tex]M=180=>0.18kg[/tex]
Charge [tex]Q=18mC=18*10^-^3C[/tex]
Velocity [tex]v=2.2m/s[/tex]
Length of Wire [tex]L=8.6cm=>0.086[/tex]
Current [tex]I=30A[/tex]
Generally the equation for Magnetic Field of Wire B is mathematically given by
[tex]B=\frac{\mu_0*I}{2\pi*l}[/tex]
[tex]B=\frac{4*3.14*10^-^7*I}{2*3.14*8.6}[/tex]
[tex]B=6.978*10^{-5}T[/tex]
Generally the equation for Force on the plane F is mathematically given by
[tex]F=qvB[/tex]
Therefore
[tex]ma=qvB[/tex]
[tex]a=\frac{qvB}{m}[/tex]
[tex]a=\frac{18*10^{-5}83.4*6.978*10^{-5}}{0.18kg}[/tex]
[tex]a=2.37*10^{-5}[/tex]
Therefore in Terms of g's
[tex]a=\frac{2.37*10^{-5}}{9.8}[/tex]
[tex]a=0.2*10^{-5}g[/tex]
The picture below shows a river flowing through a canyon.
which of the following best explains how the canyon becomes wider and deeper over time?
Answer:
Option A
Explanation:
Water posses hydraulic force and hence it carries off all the particles that lie in its way of flow.
The canyon route have rocks and soil which are first broken down by river velocity and turbulence and then carried away from their base location there by clearing way for the canyon to widen further
Hence, option A is correct
If you pitch a baseball with twice the kinetic energy you gave it in the
previous pitch, the magnitude of its momentum is
Answer:
the magnitude of momentum is √2≈ b
Explanation:
hope that helped
A force of 3 newtons moves a 10 kilogram mass horizontally a distance of 3 meters. The mass does not slow down or speed up as it moves. Which of the following must be true?
a) 9 joules of kinetic energy were produced
b) 9 joules of gravitational potential energy were produced
c) 9 joules of heat energy were produced
d) 9 joules of kinetic energy and heat were produced
Answer:
9 joules of heat energy was produced
Explanation: there is no acceleration therefore its not a kinetic energy
Energy= force × distance
= 3×3
=9
A gymnast of mass 70.0 kgkg hangs from a vertical rope attached to the ceiling. You can ignore the weight of the rope and assume that the rope does not stretch. Use the value 9.81m/s29.81m/s2 for the acceleration of gravity.
PART A Calculate the tension T in the rope if the gymnast climbs the rope at a constant rate.
PART B Calculate the tension TTT in the rope if the gymnast climbs up the rope with an upward acceleration of magnitude 1.00 m/s2
PART C Calculate the tension TTT in the rope if the gymnast slides down the rope with a downward acceleration of magnitude 1.00 m/s2m/s2 .
Answer:
43994
Explanation:
Hope this helps!
suppose a 1 square meter panel of colar cells has an efficiency of 20% and recieves the equivlent of 6 hours of direct sunlight per day. What average power, in watts, does the panel produce
Answer:
The average power per day is 1008 kW.
Explanation:
Solar constant = 1.4 kW/m2
efficiency = 20 %
area, a = 1 square meter
time = 6 hours
Energy falling on the panel in 6 hours = 1.4 x 6 x 3600 kJ
The output is
= 20 % of 1.4 x 6 x 3600
= 0.2 x 1.4 x 6 x 3600
= 6048 kJ
Average power per day is
= 6048/6 = 1008 kW
PLEASE HELP ME WITH THIS ONE QUESTION
A photon has 2.90 eV of energy. What is the photon’s wavelength? (h = 6.626 x 10^-19, 1 eV = 1.6 x 10^-19 J)
A) 677 nm
B) 218 nm
C) 345 nm
D) 428 nm
Answer:
The correct option is D.
Explanation:
The wavelength of the photon can be calculated with the following equation:
[tex] E = h\frac{c}{\lambda} [/tex]
Where:
E: is the energy of the photon = 2.90 eV
h: is the Planck's constant = 6.62x10⁻³⁴ J.s
c: is the speed of light = 3x10⁸ m/s
λ: is the wavelength
Hence, the photon's wavelength is:
[tex] \lambda = \frac{hc}{E} = \frac{6.62 \cdot 10^{-34} J*s*3.0 \cdot 10^{8} m/s}{2. 90 eV*\frac{1.6 \cdot 10^{-19} J}{1 eV}} = 428 nm [/tex]
Therefore, the correct option is D.
I hope it helps you!
How can i prove the conservation of mechanical energy?
Answer:
We can also prove the conservation of mechanical energy of a freely falling body by the work-energy theorem, which states that change in kinetic energy of a body is equal to work done on it. i.e. W=ΔK. And ΔE=ΔK+ΔU. Hence the mechanical energy of the body is conserved
Explanation:
A 4.76 kg crate is suspended from the end of a short vertical rope of negligible mass. An upward force F(t) is applied to the end of the rope, and the height of the crate above its initial position is given by y(t)=(2.80m/s)t +(0.61 m/s3 )t3
What is the magnitude of the force F when 3.71 s ?
Answer:
The magnitude of the force is 64.634 newtons.
Explanation:
According to the statement, the crate is a constant mass system, whose upward force is described by the following expression:
[tex]F(t) = m\cdot \ddot{y} (t)[/tex] (1)
Where:
[tex]F(t)[/tex] - Force, in newtons.
[tex]m[/tex] - Mass, in kilograms.
[tex]\ddot {y}(t)[/tex] - Acceleration, in meters per square second.
The function acceleration is obtained by deriving the function position twice in time:
[tex]\dot y (t) = 2.80 + 1.83\cdot t^{2}[/tex] (2)
[tex]\ddot y(t) = 3.66\cdot t[/tex] (3)
And we expand (1) by applying (3):
[tex]F(t) = 3.66\cdot m \cdot t[/tex]
Where [tex]t[/tex] is the time, in seconds.
If we know that [tex]m = 4.76\,kg[/tex] and [tex]t = 3.71\,s[/tex], then the magnitude of the force is:
[tex]F = 3.66\cdot (4.76)\cdot (3.71)[/tex]
[tex]F = 64.634\,N[/tex]
The magnitude of the force is 64.634 newtons.
List and briefly explain the incidents leading to the occurrence of any five nuclear accidents that have taken place in different parts of the world.
Answer:
Chernobyl Nuclear Disaster Nuclear Disaster. Japan 2011 Kyshtym Nuclear Disaster. Russia 1957 Windscale Fire Nuclear Disaster. Sellafield, UK 1957 Three Mile Island Nuclear Accident. Pennsylvania, USA 1979
Explanation:
Hope this helps... pls vote as brainliest
what is the difference between VELOCITY and SPEED?
Answer:
Speed is the time rate at which an object is moving along a path, while velocity is the rate and direction of an object's movement. Put another way, speed is a scalar value, while velocity is a vector. ... In its simplest form, average velocity is calculated by dividing change in position (Δr) by change in time (Δt).
Explanation:
During one trial, the acceleration is 2m/s^2 to the right. What calculation will give the tensions in actin filaments during this trial
Answer: hello your question is poorly written attached below is the complete question
answer :
TA = 1.6*10^-24 * 60 * 2, TB = 1.6*10^-24 * ( 60 + 30 ) * 2 -- ( option 1 )
Explanation:
a = 2m/s^2
Ta = m₁ a = 60 * 1.6 * 10^-24 * 2 ц
Tb - Ta = m₂ a
∴ Tb = m₂ a + Ta
= ( 30 * 1.6 * 10^-24 * 2 ) + ( 60 * 1.6 * 10^-24 * 2 )
= ( 30 + 60 ) * 1.6 * 10^-24 * 2 ц
1. Lifting an elevator 18m takes 100kJ. If doing so takes 20s, what is the average power of the elevator during the process?
2. How much work can a 0.4 hp electric mixer do in 15 s?
Answer:
1. Power = 5000 Watts
2. Workdone = 11185.5 Joules
Explanation:
Given the following data;
1. Distance = 18 m
Energy = 100 KJ = 100,000 Joules
Time = 20 seconds
To find the average power of the elevator;
Power = energy/time
Power = 100000/20
Power = 5000 Watts
2. Power = 0.4 HP
Time = 15 seconds
Conversion:
1 horsepower = 745.7 Watts
0.4 horsepower = 0.4 * 745.7 = 298.28 Watts
To find the amount of work done by the electric mixer;
Work done = power * time
Workdone = 745.7 * 15
Workdone = 11185.5 Joules
please help very easy 5th grade work giving brainliest
Answer:
the answer is option B because opposit sides of the magnets attract each other
Three wires meet at a junction. Wire 1 has a current of 0.40 A into the junction. The current of wire 2 is 0.57 A out of the junction. The current of wire 2 is 0.65 A out of the junction.
Required:
a. How many electrons per second move past a point in wire 3?
b. In which direction do the electrons move -- into or out of the junction?
Answer:
a. 1.56 × 10¹⁸ electrons per second
b. The electrons in wire 3 flow into the junction.
Explanation:
Here is the complete question
Three wires meet at a junction. Wire 1 has a current of 0.40 A into the junction. The current of wire 2 is 0.65 A out of the junction. (a) How many electrons per second move past a point in wire 3? (b) In which direction do the electrons move in wire 3 -- into or out of the junction?
Solution
(a) How many electrons per second move past a point in wire 3?
Using Kirchhoff's current law, at the junction, i₁ + i₂ + i₃ = 0 where i₁ = current in wire 1 = 0.40 A, i₂ = current in wire 2 = 0.65 A and i₃ = = current in wire 3,
So, i₃ = -(i₁ + i₂)
taking current flowing into the junction as positive and those leaving as negative, i₁ = + 0.40 A and i₂ = -0.65 A
So, i₃ = -(i₁ + i₂)
i₃ = -(0.40 A + (-0.65 A))
i₃ = -(0.40 A - 0.65 A)
i₃ = -(-0.25 A)
i₃ = 0.25 A
Since i₃ = 0.25 C/s and we have e = 1.602 × 10⁻¹⁹ C per electron, then the number of electrons flowing in wire 3 per second is i₃/e = 0.25 C/s ÷ 1.602 × 10⁻¹⁹ C per electron = 0.1561 × 10¹⁹ electrons per second = 1.561 × 10¹⁸ electrons per second ≅ 1.56 × 10¹⁸ electrons per second
(b) In which direction do the electrons move -- into or out of the junction?
Given that i₃ = + 0.25 A and that positive flows into the junction, thus, the electrons in wire 3 flow into the junction.
I’ve been stuck please help !!
Answer:
The slope of the position time graph gives the velocity.
Explanation:
The slope of the position time graph gives the value of velocity.
In first graph,
The slope is constant in both the parts but positive . So the velocity is also constant and positive for both the parts. and more than the second part, so the initial velocity is more than the final velocity.
In the second graph,
The slope is constant in both the parts but negative. So, the velocity is constant but negative for both the parts. Initial velocity is more negative than the final velocity.
According to ____________ , the randomness of the universe is constantly increasing.
a. The first law of thermodynamics
b. The zeroth law of thermodynamics
c. The second law of thermodynamics
Answer:
According to " The second law of thermodynamics", the randomness of the universe is constantly increasing?
Explanation:
So answer option C. Have a great summer.
Computer use ___code to transmit information
Binary code is the answer
Answer:
binary code is the answer of blank
Give the number of protons and the number of neutrons in the nucleus of each of the following isotopes Aluminum 25 :13 protons and 12 neutrons
Answer:
No of proton is 13 and nucleus is 13
In a certain region of space near earth's surface, a uniform horizontal magnetic field of magnitude B exists above a level defined to be y = 0. Below y = 0 , the field abruptly becomes zero (seethe figure). A vertical square wire loop has resistivity rho mass density rhom, diameter d, and side length l. It is initially at rest with its lower horizontal side at y = 0 and is then allowed to fall under gravity, with its plane perpendicular to the direction of the magnetic field.
a) While the loop is still partially immersed in the magnetic field (as it fallsinto the zero-field region), determine the magnetic "drag" forcethat acts on it at the moment when its speed is v.
b) Assume that the loop achieves a terminal velocity vt before its upper horizontal side exits the field. Determine a formulafor vt
c) If the loop is made of copper and B = 0.80 T find vt
Answer:
a) F = [tex]\frac{\pi d^2B^2lv}{16p}[/tex]
b) attached below
c) 0.037 m/s
Explanation:
a) Determine the magnetic "drag" force acting at the moment
speed = v
first step: determine current in the loop
I = [tex]\frac{\pi d^2}{16pl} B lv[/tex] ----- ( 1 )
given that the current will induce force on the three sides of the loop found in the magnetic field
forces on vertical sides = + opposite
we will cancel out
hence equation 1 becomes
F = [tex]\frac{\pi d^2B^2lv}{16p}[/tex] ( according to Lenz law we can say that the direction of force is upwards and this force will slow down the decrease in flux )
b) Determine the formula for Vt
attached below
c) Find Vt
given :
B = 0.80 T
density of copper = 8.9 * 10^3 kg/m^3
resistivity of copper = 1.68 * 10^-8 Ωm
∴ Vt = 16 ( 8.9 * 10^3 kg/m^3 ) ( 1.68 * 10^-8 Ωm ) ( 9.8 m/s^2 ) / ( 0.08 T)^2
= 0.037 m/s
A car of mass 1000 kg is moving at 25 m/s. It collides with a car of mass 1200 kg moving at 30 m/s. When the cars collide, they stick together. What is the total momentum of the system after the collision? What is the total momentum of the system before the collision? What is the velocity of the cars after the collision?
Answer:
The total momentum of the cars before the collision is 61,000 kg.m/s
The total momentum of the cars after the collision is 61,000 kg.m/s
The velocity of the cars after the collision is 27.727 m/s
Explanation:
Given;
mass of the first car, m₁ = 1000 kg
initial velocity of the car, u₁ = 25 m/s
mass of the second car, m₂ = 1200 kg
initial velocity of the second car, u₂ = 30 m/s
The common velocity of the cars after collision = v
The total momentum of the cars before collision is calculated as;
P₁ = m₁u₁ + m₂u₂
P₁ = (1000 x 25) + (1200 x 30)
P₁ = 61,000 kg.m/s
The total momentum of the cars after collision is calculated as;
P₂ = m₁v + m₂v
where;
v is the common velocities of the cars after collision since they stick together.
P₂ = v(m₁ + m₂)
To determine "v" apply the principle of conservation of linear momentum for inelastic collision.
m₁u₁ + m₂u₂ = v(m₁ + m₂)
(1000 x 25) + (1200 x 30) = v(1000 + 1200)
61,000 = 2,200v
v = 61,000/2,200
v = 27.727 m/s
The total momentum after collsion = v(m₁ + m₂)
= 27.727(1000 + 1200)
= 61,000 kg.m/s
Thus, momentum before and after collsion are equal.
At the start of a basketball game, a referee tosses a basketball straight into the air by giving it some initial speed. After being given that speed, the ball reaches a maximum height of 4.35 m above where it started. Using conservation of energy, find the height of the ball when it has a speed of 2.5 m/s.
Answer:
0.32 m.
Explanation:
To solve this problem, we must recognise that:
1. At the maximum height, the velocity of the ball is zero.
2. When the velocity of the ball is 2.5 m/s above the ground, it is assumed that the potential energy and kinetic energy of the ball are the same.
With the above information in mind, we shall determine the height of the ball when it has a speed of 2.5 m/s. This can be obtained as follow:
Mass (m) = constant
Acceleration due to gravity (g) = 9.8 m/s²
Velocity (v) = 2.5 m/s
Height (h) =?
PE = KE
Recall:
PE = mgh
KE = ½mv²
Thus,
PE = KE
mgh = ½mv²
Cancel m from both side
gh = ½v²
9.8 × h = ½ × 2.5²
9.8 × h = ½ × 6.25
9.8 × h = 3.125
Divide both side by 9.8
h = 3.125 / 9.8
h = 0.32 m
Thus, the height of the ball when it has a speed of 2.5 m/s is 0.32 m.
A soccer player kicks a ball. Why does the action force exerted by the player's foot cause a different motion than the reaction force?
The reaction force is greater than the action force.
The action force and the reaction force act on different objects.
The action force is greater than the reaction force.
The action force and the reaction force act in opposite directions.
Answer:
D because of POE
Explanation:
the reaction force is the ball exerting the same newtons of force back to your leg opposite of the ball, but the reaction force and the action force is never stronger than each-other. and action is only being done on the soccer ball, so process of elimination, the answer is D
Answer:
B
Explanation:
it can only have a different motion if it is acted upon a different ball
A projectile is launched with a velocity of 13.2 m/s at an angle of 37.0° above the horizontal.
What is the speed of the projectile at its highest point?
a. 7.94 m/s
b. 13.2 m/s
c. 10.5 m/s
d. zero
Answer:
c.
Explanation:
Given that:
The initial speed of the projective v = 13.2 m/s
The angle θ = 37.0°
At the highest point, the particle will comprise only the horizontal component of the speed because the vertical component will be zero.
So,
the horizontal component [tex]v_x = vcos \theta[/tex]
[tex]v_x = 13.2 \ m/s (cos 37^0)[/tex]
[tex]\mathsf{v_x = 10.5 \ m/s}[/tex]
Ion how to do this at all
when a temparature of a coin is 75°C, the coin's diameter increases. if the original diameter of a coin is 1.8*10^-2 m and its coefficient of linear expansion is 1.7*10^5/°C, what is the change in coins diameter?
Answer:
ΔD = 2.29 10⁻⁵ m
Explanation:
This is a problem of thermal expansion, if the temperature changes are not very large we can use the relation
ΔA = 2α A ΔT
the area is
A = π r² = π D² / 4
we substitute
ΔA = 2α π D² ΔT/4
as they do not indicate the initial temperature, we assume that ΔT = 75ºC
α = 1.7 10⁻⁵ ºC⁻¹
we calculate
ΔA = 2 1.7 10⁻⁵ pi (1.8 10⁻²) ² 75/4
ΔA = 6.49 10⁻⁷ m²
by definition
ΔA = A_f- A₀
A_f = ΔA + A₀
A_f = 6.49 10⁻⁷ + π (1.8 10⁻²)² / 4
A_f = 6.49 10⁻⁷ + 2.544 10⁻⁴
A_f = 2,551 10⁻⁴ m²
the area is
A_f = π D_f² / 4
A_f = [tex]\sqrt{4 A_f /\pi }[/tex]
D_f = [tex]\sqrt{4 \ 2.551 10^{-4} /\pi }[/tex]
D_f = 1.80229 10⁻² m
the change in diameter is
ΔD = D_f - D₀
ΔD = (1.80229 - 1.8) 10⁻² m
ΔD = 0.00229 10⁻² m
ΔD = 2.29 10⁻⁵ m
Assume that the energy lost was entirely due to friction and that the total length of the PVC pipe is 1 meter. Use this length to compute the average force of friction (for this calculation, you may neglect uncertainties).
The question is incomplete. The complete question is :
Assume that the energy lost was entirely due to friction and that the total length of the PVC pipe is 1 meter. Use this length to compute the average force of friction (for this calculation, you may neglect uncertainties).
Mass of the ball : 16.3 g
Predicted range : 0.3503 m
Actual range : 1.09 m
Solution :
Given that :
The predicted range is 0.3503 m
Time of the fall is :
[tex]$t=\sqrt{\frac{2H}{g}}$[/tex]
[tex]v_1t= 0.35[/tex] ...........(i)
[tex]v_0t= 1.09[/tex] ...........(ii)
Dividing the equation (ii) by (i)
[tex]$\frac{v_0t}{v_1t}=\frac{1.09}{035} = 3.11$[/tex]
∴ [tex]v_0=3.11 \ v_1[/tex]
Now loss of energy = change in the kinetic energy
[tex]$W=\frac{1}{2} m [v_0^2-v_1^2]$[/tex]
[tex]$W=\frac{1}{2} \times (16.3 \times 10^{-3}) \times [v_0^2-\left(\frac{v_0}{3.11}\right)^2]$[/tex]
[tex]$W=7.307\times 10^{-3} \ v_0^2$[/tex]
If f is average friction force, then
(f)(L) = W
(f) (1) = [tex]$7.307\times 10^{-3} \ v_0^2$[/tex]
(f) = [tex]$7.307\times 10^{-3} \ v_0^2$[/tex]
The Average force of friction is ( F ) = 7.307 * 10⁻³ v₀²
Given data:
Predicted range ( v₁t ) = 0.3503 m
Actual range ( v₀t ) = 1.09 m
mass = 16.3 g
First step : Determine the value of V₀
[tex]t = \sqrt{\frac{2H}{g} }[/tex] , v₁t = 0.3503 , ( v₀t ) = 1.09 m
To obtain the value of V₀
Divide ( v₀t ) by ( v₁t ) = 1.09 / 0.3503 = 3.11 v₁
∴ V₀ = 3.11 v₁
Next step : Determine the average force of friction ( f )
given that loss of energy results in a change in kinetic energy
W = [tex]\frac{1}{2} m ( vo^{2} - v1^{2} )[/tex]
= 1/2 * 16.3 * 10⁻³ * [ v₀² - [tex](\frac{v_{0} }{3.11} )^{2}[/tex] ]
∴ W = 7.307 * 10⁻³ v₀²
Average force of friction = W / Actual length
= 7.307 * 10⁻³ v₀² / 1
∴ Average force of friction ( F ) = 7.307 * 10⁻³ v₀²
Hence we can conclude that the average force of friction is 7.307 * 10⁻³ v₀²
Learn more about average force of friction : https://brainly.com/question/16207943
Your question has some missing data below are the missing data related to your question
Mass of the ball : 16.3 g
Predicted range : 0.3503 m
Actual range : 1.09 m
Consider a swimmer that swims a complete round-trip lap of a 50 m long pool in 100 seconds. What is the swimmers average speed and average velocity?
Answer:
The average speed is 1 m/s
The average velocity is 0
Explanation:
Given;
length of the pool, L = 50 m
time taken for the motion, t = 100 s
The total distance = 50 m + 50 m
The total distance = 100 m
The average speed = total distance / total time
= 100 / 100
= 1 m/s
The average velocity = change in displacement / change in time
change in displacement = 50 m - 50 m = 0
The average velocity = 0 / 100
The average velocity = 0
A two-slit interference experiment in which the slits are 0.200 mm apart and the screen is 1.00 m from the slits. The m = 1 bright fringe in the figure is 9.49 mm from the central bright fringe. Find the wavelength of the ligh
Answer:
λ = 1.90 10⁻⁶ m
Explanation:
The interference pattern for the two-slit case is
d sin θ = m λ
let's use trigonometry
tan θ = y / L
interference experiments angles are small
tan θ = sin θ /cos θ = sin θ
sin θ = y / L
we substitute
d y / L = m λ
λ = [tex]\frac{ d \ y}{m \ L}[/tex]
we calculate
λ = 0.2000 10⁻³ 9.49 10⁻³ / (1 1.00)
λ = 1.898 10⁻⁶ m
λ = 1.90 10⁻⁶ m
The wavelength of the light after calculation is find out to be λ = 1.90 *10⁻⁶ m
What is wavelength?
The distance between two successive troughs or crests is known as the wavelength. The peak of the wave is the highest point, while the trough is the lowest.The wavelength is also defined as the distance between two locations in a wave that have the same oscillation phase.
The interference pattern for the two-slit case is
d sin θ = m λ
let's use trigonometry
[tex]tan\theta=\dfrac{y}{L}[/tex]
interference experiments angles are small
[tex]sin\theta=\dfrac{y}{L}[/tex]
we substitute
[tex]\dfrac{dy}{L}=m\lambda[/tex]
[tex]\lambda=\dfrac{dy}{mL}[/tex]
we calculate
[tex]\lambda=\dfrac{0.2\times 10^{-3}\times 9.49\times 10^{-3}}{1\times 1}[/tex]
[tex]\lambda=1.90\times 10^{-6}\ m[/tex]
Hence the wavelength of the light after calculation is find out to be λ = 1.90 *10⁻⁶ m
To know more about wavelength follow
https://brainly.com/question/10728818
the speed of the bus is 40km/hr. what does it mean?
Answer:
The speed of the bus is 40 km/hr so this means the bus is travelling at a speed of 40 km per hour.
The 243000-lb space-shuttle orbiter touches down at about 236 mi/hr. The drag chute is deployed at 189 mi/hr, the wheel brakes are applied at 101 mi/hr until wheelstop, and the drag chute is jettisoned at 35 mi/hr. If the drag chute results in a deceleration of -0.000200v2 (in feet per second squared when the speed v is in feet per second) and the wheel brakes cause a constant deceleration of 3.5 ft/sec2, determine the distance s traveled from 189 mi/hr to wheelstop.
Answer:
5156.37 ft
Explanation:
Given data:
weight ( W ) = 243,000 Ib
Motion of shuttle ; from 189 mi/hr to 101 mi/hr
dv/dt = -0.0002 V^2
I/v * dv/dt = -0.0002 ds
Convert mi/hr to ft/s ( 1 mi/hr = 1.467 ft/s)
189 mi/hr = 277.263 ft/s
101 mi/hr = 148.167 ft/s
After Integrating
In ( 148.167 / 277.263 ) = -0.0002 ( S1 - S2 )
S1 - S2 = -0.627 / -0.0002
S1 - S2 = 3135 ft/s
Now from 101 mi/hr to 35 mi/hr
dv/dt = ( - 0.0002 V^2 + 3.5 )
ds = V*dv / ( -0.0002 v^2 - 3.5 )
given : 35 mi/hr = 51.345 ft/s
101 mi/hr = 148.167 ft/s
Integrate
S3 - S2 = - In( 0.0002 v^2 + 3.5 ) / 0.0002 * 2 ]
= 1644.75 ft/s
S4 - S3 = 376.62 ft/s
attached below is the remaining part of the solution
Total distance travelled = 3135 + 1644.75 + 376.62 = 5156.37 ft