Answer :
Final answer:
A runner running at 1.8 m/s can run approximately 2.943 meters in the time it takes a rock to fall from rest 100.5 meters.
Explanation:
To find the distance a runner can run in the time it takes a rock to fall, we need to determine the time it takes for the rock to fall. Using the equation v² = 2gh, where v is the final velocity of the rock (which is the same as the speed of the rock) and h is the initial height of the rock, we can calculate the time it takes for the rock to fall. From the given information, the rock falls 100.5 meters and starts from rest, so the equation becomes (1.8)² = 2(9.8)h. Solving for h, we get h = 1.635 meters. Now we can use the equation d = vt, where d is the distance, v is the velocity, and t is the time. Plugging in the known values, we get d = (1.8)(1.635) = 2.943 meters. Therefore, the runner can run approximately 2.943 meters in the time it takes the rock to fall 100.5 meters.
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