A 58.3 kg diver steps o� a diving board and
drops straight down into the water. The water
provides an average net force of resistance of
1596 N to the diver’s fall.
The acceleration of gravity is 9.81 m/s2 .
If the diver comes to rest 4.7 m below the
water’s surface, what is the total distance be-
tween the diving board and the diver’s stop-
ping point underwater? Answer in units of
m.
forceresistance(distance)=mgh
To find the total distance between the diving board and the diver's stopping point underwater, we need to calculate the distance the diver falls before coming to rest underwater.
1. Use the equation of motion to find the distance fallen:
h = (1/2)gt^2
where:
h = distance fallen
g = acceleration due to gravity (9.81 m/s^2)
t = time taken for the fall
2. Rearrange the equation to solve for time:
t = sqrt(2h / g)
3. Substitute the given values into the equation:
t = sqrt(2 * 4.7 m / 9.81 m/s^2)
4. Calculate the value of t:
t = sqrt(0.956 m) = 0.977 s (rounded to three decimal places)
5. Now, calculate the distance fallen using the formula in step 1:
h = (1/2) * g * t^2
= (1/2) * 9.81 m/s^2 * (0.977 s)^2
≈ 4.79 m
Therefore, the total distance between the diving board and the diver's stopping point underwater is approximately 4.79 meters.
To find the total distance between the diving board and the diver's stopping point underwater, we need to consider two distances: the distance the diver falls in the air and the distance the diver travels underwater.
First, let's calculate the distance the diver falls in the air using the equation for free fall:
d = (1/2) * g * t^2
where:
d is the distance fallen (unknown),
g is the acceleration due to gravity (9.81 m/s^2),
and t is the time it takes for the diver to reach the water's surface.
Since the diver drops straight down, t is the same as the time it takes for the diver to reach the stopping point underwater. We'll call this time t_tot.
Using the equation for free fall, we can rewrite it to solve for t:
t = sqrt((2 * d) / g)
Now, let's calculate t_tot using the distance the diver falls underwater (4.7 m):
t_tot = sqrt((2 * 4.7 m) / 9.81 m/s^2)
Now that we have t_tot, we can find the distance fallen in the air using the equation for free fall:
d = (1/2) * g * t_tot^2
Substituting the values:
d = (1/2) * 9.81 m/s^2 * (t_tot)^2
Finally, we can find the total distance between the diving board and the diver's stopping point underwater by adding the distance fallen in the air and the distance fallen underwater:
Total distance = d + 4.7 m
Calculating the values, we get:
t_tot = sqrt((2 * 4.7 m) / 9.81 m/s^2) = 1.067 s
d = (1/2) * 9.81 m/s^2 * (1.067 s)^2 = 5.258 m
Total distance = 5.258 m + 4.7 m = 9.958 m
Therefore, the total distance between the diving board and the diver's stopping point underwater is approximately 9.958 meters.