Rocket Height as one-dimension motion

AI Thread Summary
The discussion focuses on calculating the maximum height H reached by a rocket that accelerates upward with a constant net acceleration a until its fuel is exhausted at time t1. The maximum height can be expressed using the formula H = (1/2)at1^2, where a is the net acceleration and g is the acceleration due to gravity. For the specific case where a = 3g and t1 = 5.00 s, the calculation involves substituting g = 9.81 m/s² into the formula. The resulting maximum height is determined to be 61.3125 meters. The discussion emphasizes the importance of understanding one-dimensional motion in the context of rocket dynamics.
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A rocket, initially at rest on the ground, accelerates straight upward from rest with constant net acceleration a, until time t1, when the fuel is exhausted.

Find the maximum height H that the rocket reaches (neglecting air resistance).

Express the maximum height in terms of a, t1, and/or g. Note that in this problem, g is a positive number equal to the magnitude of the acceleration due to gravity.

That's part 1. Then comes:

If the rocket's net acceleration is a=3g for t1=5.00 s, what is the maximum height the rocket will reach? (Using 9.81 m/s^2 for g).
 
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