Maximizing Rocket Height at 1km Altitude: Solving for Acceleration and Time

[fisselt]

I know I've done this problem a few times before but I'm just a fumbling idiot at the moment..

Homework Statement

Rocket has an acceleration of 12m/s^2 and at an altitude of 1km the motor shuts off. What is the maximum height?

Homework Equations

V^2=V_i+2a(x_f-X_i)
x_f=x_i+V_i(t)+1/2at^2

The Attempt at a Solution

V^2=0+2(12)(1000)=154.92m/s
0=154.92t-9.8t^2, t=17.213s
x_f=1000+154.95(17.213)-1/2(9.8)(17.213)^2=2214.82meters


I feel like I'm doing it wrong. 12m/s^2 is the acceleration of the motor, shouldn't their be some force from gravity on the rocket while going towards 1000m?

Thanks for the help.

 

[PeterO]

I know I've done this problem a few times before but I'm just a fumbling idiot at the moment..

Homework Statement

Rocket has an acceleration of 12m/s^2 and at an altitude of 1km the motor shuts off. What is the maximum height?

Homework Equations

V^2=V_i+2a(x_f-X_i)
x_f=x_i+V_i(t)+1/2at^2

The Attempt at a Solution

V^2=0+2(12)(1000)=154.92m/s
0=154.92t-9.8t^2, t=17.213s
x_f=1000+154.95(17.213)-1/2(9.8)(17.213)^2=2214.82meters


I feel like I'm doing it wrong. 12m/s^2 is the acceleration of the motor, shouldn't their be some force from gravity on the rocket while going towards 1000m?

Thanks for the help.

The acceleration of the motor/rocket combination is the change noticed under the combined influence of the force of gravity, and the thrust force of the rocket motor, and presumably any frictional forces from the air. You are probably supposed to ignore the air resistance - a common approximation used with this sort of problem.

 

[fisselt]

thanks for the help