A rocket, initially at rest on the ground, accelerates straight upward from rest

Question

A rocket, initially at rest on the ground, accelerates straight upward from rest with constant acceleration 34.3 . The acceleration period lasts for time 5.00 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 m/(s^2)

Explanation / Answer

solution H : height a1 : acceleration before fuel ending a2 : acceleration after fuel ending V2 : initial velocity for second movement ----------------------------- 1st movement is before the fuel finishes the height that rocket travels in 1st movement can be drove by: H1= 1/2 * a1 * t^2 + V1 * t V1 = 0 --> so H1=1960 ------------------------ V3^2 - V2^2 = 2*a2*H2 V3=0 because the rocket stops moving V2 = a1*t ---> V2=343 a2= -9.8 153664=192.08*H2 H2=800 ---------- H=H1+H2----------> H=2760

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