A rocket, initially at rest on the ground, accelerates straight upward from rest with constant (net) acceleration 53.9 m/s2 . The acceleration period lasts for time 10.0 s until the fuel is exhausted. After that, the rocket is in free fall.Find the maximum height ymax reached by the rocket. Ignore air resistance and assume a constant acceleration due to gravity equal to 9.80 m/s2 .

Question
Asked Oct 10, 2019
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A rocket, initially at rest on the ground, accelerates straight upward from rest with constant (net) acceleration 53.9 m/s2 . The acceleration period lasts for time 10.0 s until the fuel is exhausted. After that, the rocket is in free fall.

Find the maximum height ymax reached by the rocket. Ignore air resistance and assume a constant acceleration due to gravity equal to 9.80 m/s2 .

 

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Expert Answer

Step 1

Initially when the engine is running, the motion of the rocket is that of an object with constant acceleration. After the fuel is exhausted, the rocket starts decelerating. The rocket’s acceleration will be equal to the negative of acceleration due to gravity.

Step 2

The rocket’s motion can be divided into two parts.

1.When the fuel is burning.

If the rocket’s initial velocity is u, acceleration is a and it travels for time t, then use Kinematics first equation to find the rocket’s velocity when the fuel is exhausted as,

V = u +at
(0m/s)+(53.9 m/s?)(10.0 s)
= 539 m/s
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V = u +at (0m/s)+(53.9 m/s?)(10.0 s) = 539 m/s

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Step 3

If distance travelled is s, then from ...

v-
2a
(539 m/s)
2(53.9 m.s2)
2695 m
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v- 2a (539 m/s) 2(53.9 m.s2) 2695 m

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