How far to the nearest tenth of a meter can a runner running at 15 m/s run in the time it takes a rock to fall from rest 76 meters?
d=vit + 1/2at^2
You know d, vi, and a, so solve for t, the time it takes the rock to hit the ground.
Multiply that time by the runner's velocity to find how far he can run in the time it takes the rock to fall from 76 meters.
To find out how far the runner can run in the given time, we need to determine the time it takes for the rock to fall from rest 76 meters. Let's divide the problem into two steps:
Step 1: Find the time it takes for the rock to fall.
We can use the kinematic equation for vertical motion:
y = (1/2) * g * t^2
Where:
y = displacement (76 meters)
g = acceleration due to gravity (approximately 9.8 m/s^2)
t = time
Rearrange the equation to solve for time (t):
t = sqrt((2 * y) / g)
t = sqrt((2 * 76) / 9.8)
t ≈ 3.91 seconds (rounded to two decimal places)
Step 2: Find how far the runner can run in the same time.
The runner's speed is given as 15 m/s. We can use the formula:
distance = speed * time
distance = 15 * 3.91
distance ≈ 58.65 meters (rounded to two decimal places)
Therefore, a runner running at 15 m/s can run approximately 58.65 meters (to the nearest tenth of a meter) in the time it takes a rock to fall from rest 76 meters.