Two Stage Rocket: Max Height Above Launch Pad

[Toranc3]

Homework Statement

In the first stage of a two-stage rocket, the rocket is fired from the launch pad starting from rest but with a constant acceleration of 3.50 m/s^2 upward. At 25.0 seconds after launch, the second stage fires for 10 seconds, which boosts the rocket's velocity to 132.5m/s upward at 35 seconds after launch. This firing uses up all the fuel, however, so after the second stage has finished firing, the only force acting on the rocket is gravity. Air resistance is negligible.

A) Find the maximum height that the stage two rocket reaches above the launch pad.

Homework Equations

y=yo + vo*t +1/2*a*t^(2)

vy=vo + a*t

The Attempt at a Solution

First stage:
y=yo + vo*t +1/2*a*t^(2)
y=1/2(3.5m/s^(2))*(25s)^(2)
y=1093.75m

Vy=Vo + a*t
Vy=3.50m/s^(2)*25s= 87.5m/s
Final velocity of first stage=87.5m/s

Second Stage:
Initial velocity of second stage=87.5m/s
vy=vo+a*t
132.5m/s=87.5m/s +a*10sec
a=4.5m/s^(2)

New acceleration=4.5m/s^(2)

y=yo + vo*t +1/2*a*t^(2)

y=1093.75m + 87.5m/s*10s + 1/2(4.5m/s^(2))*100s= 2193.75m

Is this the correct answer? Thanks!

 

[haruspex]

Yes, it looks right. It would have been slightly simpler to compute the stage two height delta by average velocity: 2s = (v₀+v_f)t
I assume there are more parts to the question.

 

[Toranc3]

Yes, it looks right. It would have been slightly simpler to compute the stage two height delta by average velocity: 2s = (v₀+v_f)t
I assume there are more parts to the question.

Thanks and yes there are more parts to this question. I am going to work on them and then post them back on here.

 

[mfb]

2193.75m is the height after the second stage finished firing - but the rocket still has a velocity upwards, and will continue to increase its height afterwards.

 

[Nickie]

Your solution looks correct! To double check, we can also use the kinematic equation for displacement without time, y= yo + 1/2* a*t^2, since we know the initial and final velocities and acceleration for the second stage. This would give us the same answer of 2193.75m. Great job on solving this problem!