± Rocket Height Part A A rocket, initially at rest on the ground, accelerates st

Question

± Rocket Height Part A A rocket, initially at rest on the ground, accelerates straight upward from rest with constant acceleration 49.0 m/s2 . The acceleration period lasts for time 8.00 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 Write your answer numerically in units of meters. Hints Submit My Answers Give Up Incorrect; Try Again; 2 attempts remaining Provide Feedback Continue

Explanation / Answer

The journey occurs in 2 main parts.
1) Rocket accelerating for 8 seconds
s = ut + 0.5at^2
s = 0.5at^2
s = 0.5 * 49 * 8^2 = 1568 m

Now calculate the speed it has reached by this point
v = u + at
v = 0 + 49 * 8 = 392 m/s

2) The continuing upward motion of the rocket, after the fuel is all gone.
v^2 = u^2 + 2as
0 = 392^2 + 2*(-9.8)*s
s = 7840 m

Now add the answer from part (1) to part (2)
total height = 9408 m

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