A 62.0 kg diver falls from rest into a swimming pool from a height of 3.50 m. It takes 1.92 s for the diver to stop after entering the water. Find the magnitude of the average force exerted on the diver during that time.
To find the magnitude of the average force exerted on the diver, we need to use the equation for average force:
Average force = change in momentum / time
In this case, to find the change in momentum, we need to first calculate the initial momentum (right before entering the water) and the final momentum (once the diver stops in the water).
The initial momentum can be calculated using the formula:
Initial momentum = mass x initial velocity
Given that the diver falls from rest, the initial velocity is 0 m/s.
Initial momentum = 62.0 kg x 0 m/s = 0 kg*m/s
To calculate the final momentum, we need to find the final velocity of the diver. Using the kinematic equation:
final velocity = initial velocity + acceleration x time
Since the diver stops, the final velocity is 0 m/s.
So, we have 0 = initial velocity + acceleration x 1.92 s
We can rearrange the equation:
acceleration = -initial velocity / time
Now, we can calculate the acceleration:
acceleration = -0 m/s / 1.92 s = 0 m/s²
Since the final velocity is 0, the change in momentum is also 0.
Change in momentum = final momentum - initial momentum = 0 - 0 = 0 kg*m/s
Finally, we can calculate the magnitude of the average force:
Average force = change in momentum / time = 0 kg*m/s / 1.92 s = 0 N
Therefore, the magnitude of the average force exerted on the diver during that time is 0 Newtons.