# Rocket in free fall

I was given the situation, 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.

I found the equation to be (1/2)a((t_1)^2)*(1+(a/g)) This formulaa is correct. I am having trouble finding the max. height that the rocket will reach. height when the net acceleration is a=3g for t1=5.00s and use g=9.81m/s^2. I tried plugging in a=3g into the equation and got and incorrect answer so i tried 2g, taking g away from the aceleration becuase of gravity downword and as well got it wrong. Im not sure what i am doing wrong

## Answers and Replies

NateTG
Science Advisor
Homework Helper
reesejm said:
I was given the situation, 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).

Hmm, you appear not to understand what 'net acceleration' means. The 'net acceleration' is the total acceleration you don't need to manipulate it any. Ergo, the height the rocket reaches is going to be:
$$\frac{1}{2}at_1^2$$

with a=3g, i plugged the numbers into $$\frac{1}{2}at_1^2$$ and got 367.9m. It said that i was off by a single numerical factor

NateTG
Science Advisor
Homework Helper
Well, unless you give the numbers, I can't check your math. You might want to check if it's looking for 368 m (because 9.81 has only 3 sig figs...)