A 42.1 kg diver steps off a diving board and
drops straight down into the water. The water
provides an average net force of resistance of
1559 N to the diver’s fall.
If the diver comes to rest 4.1 m below the
water’s surface, what is the total distance be-
tween the diving board and the diver’s stop-
ping point underwater? The acceleration due
to gravity is 9.81 m/s2 .
Answer in units of m
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To find the total distance between the diving board and the diver's stopping point underwater, we need to combine the distance the diver falls in the air and the distance they travel underwater.
First, let's determine the distance the diver falls in the air. We can use the kinematic equation:
d = (1/2) * g * t^2
Where:
d is the distance fallen
g is the acceleration due to gravity (9.81 m/s^2)
t is the time it takes the diver to reach the water's surface.
Since the diver is in free fall until they hit the water, we need to find the time it takes for the diver to reach the water's surface. We can use the following kinematic equation:
vf = vi + g * t
Where:
vf is the final velocity (0 m/s since the diver comes to rest in the water)
vi is the initial velocity (0 m/s since the diver drops vertically)
g is the acceleration due to gravity (9.81 m/s^2)
t is the time it takes for the diver to reach the water's surface.
Rearranging the equation, we have:
t = vf / g
Substituting the values, we get:
t = 0 / 9.81
t = 0 seconds (since the velocity is initially 0, the time will also be 0)
Since the time is 0, the diver falls instantly into the water without any additional time in the air. Therefore, the distance fallen in the air is 0 meters.
Now let's calculate the distance the diver travels underwater. We can use another kinematic equation:
d = vi * t + (1/2) * a * t^2
Where:
d is the distance traveled underwater
vi is the initial velocity (0 m/s since the diver comes to rest in the water)
a is the acceleration due to gravity (9.81 m/s^2, acting in the opposite direction)
t is the time it takes for the diver to come to rest underwater.
We can rearrange the equation to solve for t:
t = sqrt((2 * d) / a)
Substituting the values, we get:
t = sqrt((2 * 4.1) / 9.81)
t ≈ 0.637 s
Now we can calculate the distance traveled underwater:
d = vi * t + (1/2) * a * t^2
d = 0 * 0.637 + (1/2) * 9.81 * (0.637)^2
d ≈ 2.024 m
Finally, the total distance between the diving board and the diver's stopping point underwater is the sum of the distance fallen in the air (0 m) and the distance traveled underwater (2.024 m):
Total distance = 0 + 2.024
Total distance ≈ 2.024 m
So, the total distance between the diving board and the diver's stopping point underwater is approximately 2.024 meters.