Find Maximum Elevation of Test Rocket

[jenc305]

This problem seems simple but I'm just not getting the correct answer, please help thank you.

A test rocket is fired straigt up from rest with a net accerleration of 20m/s^2. After 4 seconds the motor turns off, but the rocket continues to coast upward. What maximum elevation does the rocket reach?

This is what I get

X_0=0, a=20m/s^2, t=4 s

1/2(20m/s^2)(4 s)^2=160m (the correct answer is 487m )

 

[hotvette]

You need to think of it as 2 separate problems.

1. Rocket under the stated acceleration

2. Rocket after acceleration stops.

The final conditions of problem 1 (i.e. height and velocity) are the initial conditions for problem 2.

 

[jenc305]

Problem 1
x=160m and v=80m/s

Problem 2
x_0=160m, v_0=80m/s, a=?
if it stopped accelerating, I would assume that the acceleration would be decreasing as the rocket coasted upward. Would this be correct?

 

[hotvette]

So far, so good. You have the initial conditions for problem #2. Now, you need the equation of motion (in the vertical direction) for a projectile with initial conditions of distance and velocity. You must have been given such an equation or taught how to derive it using F=ma.

 

[jenc305]

Thank you. This is what I got

160m-[0-(80m/s)^2/2(9.8m/s^2)]=486.5m

Also, I had another question about horizontal projectile motion.
Why does the distance of two packages steadily increase as they fall out of a plane going at constant speed.

I thought the distance would remain constant between the two packages as they fall when air friction is negligible. I can't make sense of it.