how far to the nearest tenth of a meter can a runner running at 7.9 m/s run in the time it takes a rock to fall from rest 65 meters?
First compute the time to fall:
T = sqrt(2H/g).
You should get between 3 and 4 secinds.
Then multiply T by 7.9 m/s.
To determine how far the runner can run in the given time, we need to find the time it takes for the rock to fall from rest 65 meters. Let's assume that the acceleration due to gravity is approximately 9.8 m/s².
Using the equation of motion for an object in free fall, we can find the time it takes for the rock to fall:
h = (1/2) * g * t²
Where:
h = height (65 meters)
g = acceleration due to gravity (9.8 m/s²)
t = time
Rearranging the equation, we get:
t = sqrt(2h / g)
t = sqrt(2 * 65 / 9.8)
t ≈ sqrt(13.27)
t ≈ 3.64 seconds
Now that we have the time, we can determine how far the runner can go in that time. We can use the equation:
distance = speed * time
distance = 7.9 m/s * 3.64 s
distance ≈ 28.76 meters
Therefore, the runner can run approximately 28.76 meters in the time it takes for the rock to fall from rest 65 meters. To the nearest tenth of a meter, the runner can run approximately 28.8 meters.