How far to the nearest tenth of a meter can a runner running at 10 m/s run in the time it takes a rock to fall from rest 99 meters?
99 = 4.9 t^2
t = 4.495 s
10 * 4.495 = 44.95m = 45.0 m to nearest tenth
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To calculate the distance a runner can cover in the time it takes a rock to fall, we need to determine the time it takes for the rock to fall 99 meters.
The formula to calculate the time it takes for an object to fall freely is given by the equation:
d = (1/2) * g * t^2
Where:
d = distance (99 meters in this case)
g = acceleration due to gravity (approximately 9.8 m/s^2)
t = time taken
Rearranging the equation to solve for time:
t^2 = (2 * d) / g
t^2 = (2 * 99) / 9.8
t^2 = 2 * 10.102
t ≈ √(20.204)
t ≈ 4.5 seconds (rounded to one decimal place)
Therefore, the time it takes for the rock to fall is approximately 4.5 seconds.
Now, we can calculate the distance the runner can cover in that time.
distance = speed * time
distance = 10 m/s * 4.5 seconds
distance = 45 meters
Therefore, the runner can run approximately 45 meters in the time it takes for the rock to fall 99 meters.