How far to the nearest tenth of a meter can a runner running at 11 m/s run in the time it takes a rock to fall from rest 78 meters?

Question

How far to the nearest tenth of a meter can a runner running at 11 m/s run in the time it takes a rock to fall from rest 78 meters?

Answer 1

Compute the fall time

t = sqrt(2H/g)
and multiply it by the runner's speed.

H = 78 m
g = 9.8 m/s^2

Answer 2

Well, that's a rock solid question! Let's calculate it with a dash of laughter.

So, we know that the rock falls from rest 78 meters. Assuming the runner continues running at a constant speed of 11 m/s, we can use the equation:

Distance = Speed × Time

Now, let's find out how long it takes for the rock to fall. We can use the equation:

Distance = (1/2) × Gravity × Time²

Since the rock starts from rest, its initial velocity is 0, making the equation simpler:

Distance = (1/2) × Gravity × Time²

Now, let's solve for Time. With a giggle, we can rearrange the equation:

Time = √(2 × Distance / Gravity)

To the nearest tenth of a meter, the runner can run:

Distance = Speed × Time
Distance = 11 m/s × √(2 × 78 m / (9.8 m/s²))

Calculating that with a pinch of mathematics, we find the runner can run approximately 61.8 meters.

So, the answer is approximately 61.8 meters. I hope this distance makes you runner-eously happy!

Answer 3

To determine the distance covered by the runner, we need to find the time it takes for the rock to fall 78 meters and then use that time to compute the distance covered by the runner.

First, let's find the time it takes for the rock to fall 78 meters using the formula for free fall:

h = 0.5 * g * t^2

Where:
h is the height (78 meters)
g is the acceleration due to gravity (approximately 9.8 m/s^2)
t is the time (unknown)

Rearranging the formula to solve for t:

t^2 = (2 * h) / g

t^2 = (2 * 78) / 9.8
t^2 = 15.918367346938776

Taking the square root of both sides:

t = √15.918367346938776
t ≈ 3.98997487421324 seconds

Now, we can calculate the distance covered by the runner using the formula:

distance = speed * time

distance = 11 m/s * 3.98997487421324 s
distance ≈ 43.88972461535564 meters

Therefore, the runner can run approximately 43.9 meters in the time it takes for the rock to fall from rest 78 meters.