Physics
Physics
5th Edition
ISBN: 9781260487008
Author: GIAMBATTISTA, Alan
Publisher: MCGRAW-HILL HIGHER EDUCATION
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Chapter 2, Problem 68P

(a)

To determine

What is the rocket’s altitude when the engine fails?

(a)

Expert Solution
Check Mark

Answer to Problem 68P

Rocket’s altitude when the engine fails is 25km.

Explanation of Solution

Write the equation to find the displacement of rocket.

s=ut+12at2                   (I)

Here, u is the initial velocity, s is the altitude, t is the time, a is the acceleration of the rocket.

The initial velocity of rocket is zero, therefore, rewrite equation (I)

s=12at2 (II)

Conclusion

Substitute 20m/s2 for a and 50s for t in equation (II) to get s.

s=12(20m/s2)(50s)2=25km

Therefore, Rocket’s altitude when the engine fails is 25km.

(b)

To determine

When does the rocket reach the maximum height?

(b)

Expert Solution
Check Mark

Answer to Problem 68P

The rocket will reach maximum height at 152s.

Explanation of Solution

Write the equation to find the final velocity of the rocket.

vy=viygΔt=aΔt1gΔt (I)

Here, vy is the final velocity of rocket, a is the acceleration, Δt1 is the change in time, g is the acceleration due to gravity

The final velocity of rocket is zero. Hence rewrite equation (I).

0=aΔt1gΔtΔt=agΔt1 (II)

Conclusion:

Substitute 20m/s2 for a , 9.80m/s2 for g , and 50s for Δt1 in  equation (II) to get Δt.

Δt=(20m/s2)(9.8m/s2)(50s)=102s

Therefore, The rocket will reach maximum height at 152s.

(c)

To determine

What is the maximum height reached by the rocket?

(c)

Expert Solution
Check Mark

Answer to Problem 68P

The maximum height reached by rocket is 76km.

Explanation of Solution

Write the equation to find the maximum height reached by the rocket.

yf=yi+viyΔt12g(Δt)2 (I)

Here, yf is the maximum height, yi is the initial height, viy is the initial velocity, Δt is the change in time, g is acceleration due to gravity

Substitute agΔt1 for Δt , and aΔt for viy in equation (I).

yf=yi+(aΔt1)(agΔt1)12g(agΔt1)2 (II)

Solve equation (II) to get yf.

yf=yi+a2(Δt1)2ga2(Δt1)22g=yi+a2(Δt1)22g (III)

Conclusion:

Substitute 25km for yi , 20m/s2 for a , 50s for Δt , 9.8m/s2 for g in equation (III) to get yf.

yf=25km+(20m/s2)2(50s)22(9.8N/kg)=76km

Therefore, The maximum height reached by rocket is 76km.

(d)

To determine

What is the velocity of the rocket just before it hits the ground?

(d)

Expert Solution
Check Mark

Answer to Problem 68P

The velocity of the rocket just before it hits the ground is 1220m/s downwards.

Explanation of Solution

Write the equation to find the final velocity of rocket.

vfy2=viy22gΔy (I)

Here, vfy is the final velocity, viy is the initial velocity, g is the acceleration due to gravity, Δy is the displacement

The initial velocity of the rocket is zero. Hence rewrite equation (I) to get vfy.

vfy=2gΔy (II)

Conclusion:

Substitute 9.8m/s2 for g , and 76km for Δy in equation (II) to get vfy.

vfy=2(9.8m/s2)(076×103m)=1220m/s

Therefore, The velocity of the rocket just before it hits the ground is 1220m/s downwards.

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Chapter 2 Solutions

Physics

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