# Altitude of rocket with 2E5 N thrust

#### astenroo

1. The problem statement, all variables and given/known data

A polaris missile has a mass of 1.4 x 10^4 kg and its engine has a thrust of 2 x 10^5 N. If its engines fire in the vertical direction for 1 min starting from rest, to what vertical height would it rise in the absence of air resistance?

2. Relevant equations

F=ma
W=mg
y=.5at^2

3. The attempt at a solution

So, I figured F-W=ma, where a is the upward acceleration, F is the thrust, W is the wight of the rocket and m is the mass of the rocket. This would produce a total upward acceleration of a= (F-W)/m=4.49 m/s^2. The distance y is then y=0.5 x 4,49 x 60^2=8074 m. The correct answer should be 11.8 km (3.7 km in free fall).

Where am I thinking wrong here?

#### astenroo

I have to find the velocity after its engine shuts down. The final velocity should be 0, so taking the following equation v^2=v0^2-2g(x-x0), where v0 is the velocity when the engines shut down, x0 is the altitude gained during thrust phase.
x=(v0^2)/2g + x0 = roughly 11.8 km.

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