Altitude of rocket with 2E5 N thrust

AI Thread Summary
The discussion revolves around calculating the altitude of a Polaris missile with a thrust of 2 x 10^5 N and a mass of 1.4 x 10^4 kg, firing vertically for one minute without air resistance. The upward acceleration is determined to be 4.49 m/s² after accounting for the weight of the rocket. The initial calculation yields a height of 8074 m, but the correct altitude, considering the missile's free fall after engine shutdown, is approximately 11.8 km. The final velocity at engine shutdown is crucial for determining the total altitude, factoring in the height gained during the thrust phase. The discussion emphasizes the importance of correctly applying kinematic equations to achieve the accurate result.
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Homework Statement



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?

Homework Equations



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

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?
 
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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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