Solving a 1974 kg Weather Rocket Mystery

AI Thread Summary
To solve the weather rocket mystery, the first step is to determine the rocket's acceleration during the initial 20.27 seconds of powered flight. After the motor stops, the rocket experiences free fall with a constant acceleration of -g. The altitude of 7242 meters at 23.94 seconds can be calculated by combining the equations of motion for both phases of the flight. Key equations to consider include those for displacement and velocity under constant acceleration. The final calculations will yield both the initial acceleration and the speed of the rocket as it reaches the specified altitude.
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Lost please help!

A 1974 kg weather rocket is launched straight up. The rocket motor provides a constant acceleration for 20.27 s, then the motor stops. The rocket altitude 23.94 s after launch is 7242. You can ignore any effects of air resistance.

What was the rocket's acceleration during the first 20.27 s?
What is the rocket's speed as it passes through a cloud 7242 m above the ground?
 
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The rocket is under a constant acceleration (call it 'a') during the first part of the trip (the first 20.27 secs), and under a constant acceleration of -g thereafter. You just have to splice these two solutions together. What equations do you know that govern motion under constant acceleration?
 
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