How far to the nearest tenth of a meter can a runner running at 15 m/s run in the time it takes a rock to fall from rest 68 meters?
neglecting air resistance of course...
t=sqrt(68/9.81m/s^2) this of course may vary with g, or where the rock is dropped.
distance=15*timeabove to the nearest tenth.
To find out how far the runner can run in the given time, we need to determine the time it takes for the rock to fall 68 meters.
We can use the equation of motion for an object in free fall:
s = ut + (1/2)gt^2
where:
s is the distance traveled
u is the initial velocity (0 m/s since the rock starts from rest)
t is the time taken
g is the acceleration due to gravity (approximately 9.8 m/s^2)
Rearranging the equation to solve for time, we have:
t = √((2s)/g)
Plugging in the values, we get:
t = √((2 * 68) / 9.8)
t ≈ √(138.7755)
t ≈ 11.77 seconds (rounded to two decimal places)
Now that we have the time it takes for the rock to fall, we can calculate how far the runner can run at a speed of 15 m/s in that time:
Distance = Speed × Time
Distance = 15 m/s × 11.77 s
Distance ≈ 176.55 meters
Therefore, the runner can run approximately 176.55 meters in the time it takes for the rock to fall from rest 68 meters.
In terms of the nearest tenth of a meter, we round the distance to one decimal place:
Distance ≈ 176.6 meters (rounded to the nearest tenth of a meter).