At the local swimming hole, a favorite trick is to run horizontally off a cliff that is 5.95 m above the water. One diver runs off the edge of the cliff, tucks into a "ball," and rotates on the way down with an average angular speed of 2.55 rev/s. Ignore air resistance and determine the number of revolutions she makes while on the way down.
d = 0.5g*t^2 = 5.95 m.
4.9t^2 = 5.95
t^2 = 1.21 s.
t = 1.10 s.
2.55rev/s * 1.1s = 2.8 revs.
To determine the number of revolutions the diver makes while on the way down, we need to calculate the time it takes for the diver to reach the water first.
We can use the kinematic equation for displacement to find the time taken to fall from a height:
h = (1/2)gt^2
Where:
h is the height (5.95 m)
g is the acceleration due to gravity (9.8 m/s^2)
t is the time taken
Rearranging the equation to solve for t:
t = sqrt(2h/g)
Now, we can plug in the given values:
t = sqrt(2 * 5.95 / 9.8)
t ≈ 1.09 s
Now, we can calculate the number of revolutions the diver makes using the given average angular speed:
Number of revolutions = angular speed * time taken
Number of revolutions = 2.55 rev/s * 1.09 s
Number of revolutions ≈ 2.78 revolutions
Therefore, the diver makes approximately 2.78 revolutions while on the way down.