How far to the nearest tenth of a meter can a runner running at 9 m/s run in the time it takes a rock to fall from rest 73 meters?
To find the answer, we need to determine the time it takes for the rock to fall from rest 73 meters, and then calculate how far the runner can run in that time.
First, we can find the time it takes for the rock to fall using the equation of motion:
h = (1/2) * g * t^2
Where:
h = 73 meters (height of the fall)
g = 9.8 m/s^2 (acceleration due to gravity)
t = time
Rearranging the equation, we get:
t^2 = (2 * h) / g
t^2 = (2 * 73) / 9.8
t^2 = 146 / 9.8
t^2 ≈ 14.898
Next, we take the square root of both sides to find t:
t ≈ √14.898
t ≈ 3.86 seconds
Now that we have the time it takes for the rock to fall, we can calculate the distance the runner can run using the equation:
distance = speed * time
distance = 9 m/s * 3.86 seconds
distance ≈ 34.74 meters
Therefore, the runner can run approximately 34.74 meters in the time it takes the rock to fall from rest 73 meters.