Solving Newton's Laws Problem: Baseball Player & Runner

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A baseball player hits a ball straight up at 18.0 m/s, and the runner on third base starts running towards home plate, which is 27.4 m away. To solve the problem, it's essential to determine how long the ball takes to return to its initial height, which can be calculated using the formula for free fall. The time for the ball to ascend and descend is approximately 3.67 seconds. Given the runner's speed of 7.60 m/s, he will cover about 27.4 m in approximately 3.61 seconds, meaning he will reach home plate just before the ball returns. The runner will be slightly ahead of home plate when the ball descends back to its original height.
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Homework Statement



A baseball player hits the ball straight up in the air with a velocity of 18.0m/s. As soon as the ball is hit, the runner on third base dashes toward the home plate. The distance between third base and home plate is 27.4m. Where will the runner be with reference to home plate when the ball returns to its initial height?

Homework Equations


I am not sure

The Attempt at a Solution


Dont understand how to start the solution
 
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How long does it take for the ball to come down? How far does the guy run in this time? (Note that without the speed of the runner, it's impossible to answer this question. The answer will be very different if he's running at the speed of continental drift than if he's running at the speed of light)
 
The guy runs at 7.60 m /s
 
OK, so how long does it take for the ball to come down?
 
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