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Classical Mechanics

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After What Time Will Two Sky Divers Catch Up with Each Other?

CLMECH-@PX4K0

Tom, who is taking sky-diving lessons, and his instructor, Carol, jump out of the plane at the same time, but separately from each other. Carol starts falling in the spread-eagle form and Tom starts falling head-first as shown in the figure below.

D. Dalafave Created for Albert.io. Copyright 2016. All rights reserved.

As a result, Carol falls with an acceleration of $4.7 \space m/s^2$, while Tom falls with a greater acceleration of $6.2 \space m/s^2$. After $4.5 \space s$ of falling at this acceleration, Tom assumes the spread-eagle form and continues to fall at a smaller, constant acceleration of $3.6 \space m/s^2$.

At the same instant, Carol changes her form to head-first. She tries to catch up with Tom by moving toward him with a constant acceleration of $7.6 \space m/s^2$. Assume that both Tom and Carol are moving along the same vertical line and that they jumped out of the plane with zero initial velocity.

How much time (in seconds) after jumping from the plane will Carol catch up with Tom?