A high diver of mass 65.0 kg steps off a board 10.0 m above the water and falls vertical to the water, starting from rest. If her downward motion is stopped 2.30 s after her feet first touch the water, what average upward force did the water exert on her?
I'm not sure how to go about solving this. I've tried a few different ways but none of them yielded the right answer. Please help.
The average upward force exerted by the water on the diver is 13,043 N.
To solve this problem, we can use the equation F = ma, where F is the force, m is the mass, and a is the acceleration. We can rearrange this equation to solve for the force: F = m * a.
We know the mass of the diver (m = 65.0 kg) and the time it took for her downward motion to be stopped (t = 2.30 s). We can calculate the acceleration by using the equation a = v/t, where v is the final velocity. Since the diver started from rest, her final velocity is the same as her downward velocity, which is 10.0 m/s. Therefore, a = 10.0 m/s / 2.30 s = 4.35 m/s^2.
Plugging this into the equation F = m * a, we get F = 65.0 kg * 4.35 m/s^2 = 13,043 N.
To solve this problem, we can use the formula for average force:
Average Force = Change in Momentum / Time Interval
First, we need to find the change in momentum of the high diver. Since the initial velocity of the diver is zero and the final velocity is unknown, we can use the equation of motion to find the final velocity:
vf = vi + at
Here, vi is the initial velocity, which is zero, a is the acceleration, and t is the time interval, which is given as 2.30 s. In this case, the acceleration is due to gravity, so a = 9.8 m/s^2 (acceleration due to gravity near the surface of the Earth).
Using the equation:
vf = vi + at
vf = 0 + (9.8 m/s^2)(2.30 s)
vf = 22.54 m/s
Next, we need to calculate the initial momentum (pi) and final momentum (pf) of the diver:
pi = m * vi
pf = m * vf
Since the initial velocity is zero:
pi = 0
pf = m * vf
Now, we can calculate the change in momentum:
Change in Momentum = pf - pi
Change in Momentum = m * vf - 0
Change in Momentum = m * vf
Substituting the given values:
Change in Momentum = (65.0 kg)(22.54 m/s)
Change in Momentum = 1465.1 kg⋅m/s
Finally, we can calculate the average upward force exerted by the water on the diver using the formula:
Average Force = Change in Momentum / Time Interval
Average Force = 1465.1 kg⋅m/s / 2.30 s
Average Force ≈ 637.4 N
Therefore, the average upward force exerted by the water on the diver is approximately 637.4 N.
To solve this problem, you can use the equations of motion to calculate the average upward force exerted by the water on the diver.
Step 1: Find the time it takes for the diver to fall 10.0 m.
Use the equation for displacement of an object in free fall:
s = (1/2)gt^2
Here, s = 10.0 m and g = 9.8 m/s^2 (acceleration due to gravity).
Rearranging the equation, we get:
t^2 = (2s) / g
t^2 = (2 * 10.0) / 9.8
t^2 = 2.04
t = √2.04
t ≈ 1.43 s
Step 2: Find the time taken after the feet touch the water until the downward motion stops.
Given that the time taken is 2.30 s.
Step 3: Calculate the time taken for the upward motion.
The time taken for the upward motion can be calculated by subtracting the time taken in Step 2 from the time taken in Step 1:
Time taken for the upward motion = 1.43 s - 2.30 s = -0.87 s
Step 4: Calculate the average acceleration during the upward motion.
The average acceleration during the upward motion is given by:
a = (Change in velocity) / (Time taken)
Since the diver starts from rest, the change in velocity is the final velocity.
Using the formula v = u + at, where u is the initial velocity and a is the acceleration, we get:
0 = (0) + a(-0.87)
a = 0 m/s^2 (since the time taken is negative, the acceleration is zero)
Step 5: Calculate the average upward force exerted by the water.
The average upward force exerted by the water can be calculated using Newton's second law of motion:
F = ma
Since the mass of the diver is 65.0 kg and the acceleration is 0 m/s^2, we get:
F = 65.0 kg * 0 m/s^2
F = 0 N
Therefore, the average upward force exerted by the water on the diver is 0 N.