A rocket is launched straight up with constant acceleration. Four seconds after liftoff, a bolt falls off the side of the rocket. The bolt hits the ground 6.0s{\rm s} later.What was the rocket's acceleration?
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To find the rocket's acceleration, we need to use the equations of motion and kinematics.
Let's break down the problem step by step.
1. First, we need to determine the time it took for the bolt to hit the ground after falling off the rocket. We are given that the bolt hit the ground 6.0 seconds later.
2. The bolt fell off 4.0 seconds after the launch. Therefore, the time it took for the bolt to fall is the difference between these two times: 6.0s - 4.0s = 2.0s.
3. We know that the bolt falls under the influence of gravity, which has an acceleration of approximately 9.8 m/s² in the downward direction (assuming no air resistance).
4. We can use the equation of motion for a falling object: s = ut + (1/2)at², where s is the distance fallen, u is the initial velocity (which is zero for a falling object), t is the time taken, and a is the acceleration.
5. In this case, we are trying to find the acceleration, so we rearrange the equation to solve for a: a = 2s / t².
6. Plugging in the values for s = 0 (since the bolt fell from rest) and t = 2.0s, we can calculate the acceleration: a = 2(0) / (2.0s)² = 0 m/s².
Therefore, the rocket's acceleration is 0 m/s². This means that the rocket is not accelerating vertically, but instead moving at a constant velocity or already in a state of free fall.