How far to the nearest meter can a sprinter running at 9 m/s, travel in the time it takes a rock to fall 28 meters
To find out how far the sprinter can travel in the given time, we need to determine the time it takes for the rock to fall 28 meters.
First, let's calculate the time it takes for the rock to fall 28 meters using the equation for free fall:
h = (1/2) * g * t^2
Where:
h is the height (28 meters),
g is the acceleration due to gravity (approximately 9.8 m/s^2), and
t is the time it takes for the rock to fall.
Rearranging the equation to solve for t:
t^2 = (2h) / g
Substituting the given values:
t^2 = (2 * 28) / 9.8
t^2 ≈ 5.71
Taking the square root of both sides:
t ≈ √5.71
t ≈ 2.39 seconds (rounded to two decimal places)
Now that we know the time it takes for the rock to fall, we can calculate the distance the sprinter can travel in that time.
Distance = speed * time
Distance = 9 m/s * 2.39 s
Distance ≈ 21.51 meters
Therefore, the sprinter can travel approximately 21.51 meters in the time it takes for the rock to fall 28 meters.