A rocket, initially at rest on the ground, accelerates straight upward from rest with constant acceleration 44.1m/s^2. The acceleration period lasts for time 7.00s until the fuel is exhausted. After that, the rocket is in free fall. Find the maximum height y_max reached by the rocket. Ignore air resistance and assume a constant acceleration due to gravity equal to 9.80 rm{m/s^2}.

Question

Physics

Kiana Sanchez

3 May, 09:24

A rocket, initially at rest on the ground, accelerates straight upward from rest with constant acceleration 44.1m/s^2. The acceleration period lasts for time 7.00s until the fuel is exhausted. After that, the rocket is in free fall. Find the maximum height y_max reached by the rocket. Ignore air resistance and assume a constant acceleration due to gravity equal to 9.80 rm{m/s^2}.

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Elian Ayala · Answer 1

The acceleration and distance is related to the following expression:

y=v0*t + a*t^2/2; v0=0

y=44.1*100/2 = 2205m

hence, the speed will be

v=0 + a*t = 441m/s

from that height it will just be subjected to the gravitational acceleration

0=v_acc^2 - 2g*y_free

y_free = v_acc^2/2g = 9922.5m

y_max = y_acc+y_free = 441+9922.5 = 10363.5m