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 91 meters
Use kinematics to find the time it will take the rock to fall to the ground.
(delta)x = V(initial)(time) + .5at^2
(delta)x = 0 + .5(-9.8)t^2
First term drops out because initial velocity is zero.
Acceleration is that due to gravity.
Negative sign is because it is accelerating downward, so technically the (delta)x will be negative as well so that you will not be square rooting a negative number.
You should be able to get it from here.
20.5
To calculate the distance that a runner can run in a given time, we need to use the formula:
Distance = Speed x Time
In this case, the runner is running at a speed of 10 m/s. Let's assume the time it takes for the rock to fall from rest is the same amount of time it takes the runner to run a certain distance.
The distance the rock falls is given as 91 meters. So we can set up the equation:
Distance (runner) = Speed x Time (runner)
Distance (rock) = 91 meters
Since we want to find the distance the runner can run, we rearrange the formula:
Time (runner) = Distance (rock) / Speed (runner)
Plugging in the values:
Time (runner) = 91 meters / 10 m/s
Time (runner) = 9.1 seconds
Now that we know the time (runner), we can calculate the distance the runner can run:
Distance (runner) = Speed (runner) x Time (runner)
Distance (runner) = 10 m/s x 9.1 seconds
Distance (runner) = 91 meters
Therefore, the runner can run a distance of 91 meters in the same time it takes the rock to fall from rest 91 meters.
To answer the question of how far to the nearest tenth of a meter the runner can run, we calculate the distance as:
Distance (runner) = Speed (runner) x Time (runner)
Distance (runner) = 10 m/s x 9.1 seconds
Distance (runner) = 91 meters
Therefore, the runner can run a distance of 91 meters to the nearest tenth of a meter.