A rocket, initially at rest on the ground, accelerates straight upward from rest with constant acceleration 58.8m/s2 . 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 ymax reached by the rocket. Ignore air resistance and assume a constant acceleration due to gravity equal to 9.80 m/s2 .

Question

A rocket, initially at rest on the ground, accelerates straight upward from rest with constant acceleration 58.8m/s2 . 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 ymax reached by the rocket. Ignore air resistance and assume a constant acceleration due to gravity equal to 9.80 m/s2 .

trantom · Answer

well for accelerations, there is a simple way to find a relationship between time and distance, which is the number (58.8 in this case) divided by two times time squared equals distance.

trantom · Answer

so, in this case it is 29.4t^2=d

trantom · Answer

so, take your time of 7 seconds, plug it in for t, and you got your answer!

trantom · Answer

now keep in mind that you have to make the time units the same, so you cant use kilometers per hour and seconds, you have to use some distance per some time and the SAME UNIT OF TIME for t. Also, distance is the SAME UNIT OF DISTANCE as was in your acceleration expression (in your case, the acceleration expression was 58.8 m/s^2)

trantom · Answer

@polychapa