Finding the maximum height of a rocket

[hieule]

A rocket, initially at rest on the ground, accelerates straight upward from rest with constant net acceleration a, until time t_1, 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, t_1, and/or g. Note that in this problem, g is a positive number equal to the magnitude of the acceleration due to gravity.

my answer is:
(at)^2/2g +1/2at^2

is that correct yet?

 

[adrianx]

A rocket, initially at rest on the ground, accelerates straight upward from rest with constant net acceleration a, until time t_1, 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, t_1, and/or g. Note that in this problem, g is a positive number equal to the magnitude of the acceleration due to gravity.

my answer is:
(1/2)*(g)*(t1)^2

but that is incorrect

Your equation only shows the distance as far as when the fuel is gone. A rocket's path is a parabola.. when it shoots up and then runs out of fuel, it will go up a little more and then start to fall.

 

[wais]

Yes, your answer is correct. The maximum height reached by the rocket can be expressed as (at)^2/2g +1/2at^2, where a is the constant acceleration, t is the time at which the fuel is exhausted, and g is the acceleration due to gravity. This formula takes into account the initial velocity of the rocket (which is zero) and the fact that the rocket is accelerating both due to its own engine and the force of gravity.