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 90 meters?
obviously some people find these hard or they wouldn't be asking them.
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To determine how far the rock falls, we can use the formula for free fall:
h = (1/2) * g * t^2
Where:
- h is the height, which is 90 meters in this case.
- g is the acceleration due to gravity, approximately equal to 9.8 m/s^2.
- t is the time it takes for the rock to fall.
Rearranging the formula, we can solve for t:
t = sqrt((2 * h) / g)
Plugging in the given values:
t = sqrt((2 * 90) / 9.8)
t ≈ 4.22 seconds
Now, let's calculate how far the runner can run in that time. We can use the formula:
d = v * t
Where:
- d is the distance covered by the runner.
- v is the velocity of the runner, which is 11 m/s.
- t is the time taken, which is 4.22 seconds.
Substituting the values:
d = 11 * 4.22
d ≈ 46.42 meters
Therefore, the runner can run approximately 46.42 meters in the time it takes for the rock to fall 90 meters. Rounded to the nearest tenth of a meter, the answer is approximately 46.4 meters.
Calculate the time t it takes a rock to fall 90 m.
90 = (1/2) g t^2
Multiply that time by 11 m/s.
These questions are not hard. You need to show some work of your own.