A 55.0 kg diver steps off a diving board and drops straight down into the water. The water provides an upward average net force 1480 N. If the diver comes to rest 5.6 m below the water's surface, what is the total distance between the diving board and the diver's stopping point underwater?
To find the total distance between the diving board and the diver's stopping point underwater, we need to consider two factors: the distance traveled while falling freely and the distance traveled while decelerating in the water.
First, let's find the distance traveled while falling freely. We can use the equation of motion for free fall:
s = ut + (1/2)at^2
Where:
s is the distance
u is the initial velocity (which is zero since the diver is at rest initially)
a is the acceleration due to gravity (-9.8 m/s^2)
t is the time
Since the diver falls straight down, we can assume that the initial time is zero and the final time is the time it takes for the diver to reach the water's surface. We can calculate the time using the equation:
v = u + at
Where:
v is the final velocity (which is also zero since the diver comes to rest)
u is the initial velocity (which is zero)
a is the acceleration due to gravity (-9.8 m/s^2)
t is the time
Rearranging the equation, we have:
t = -u/a
Substituting the given values, we get:
t = -0/(-9.8) = 0 seconds
This means that the diver reaches the water's surface instantaneously.
Now, let's find the distance traveled while decelerating in the water. The net force acting on the diver is equal to the buoyant force provided by the water, given by:
F_net = F_buoyant = ρ * V * g
Where:
F_net is the net force
F_buoyant is the buoyant force
ρ is the density of water (taken as 1000 kg/m^3)
V is the volume of the diver
g is the acceleration due to gravity (-9.8 m/s^2)
The volume of the diver can be calculated using the relationship between mass, density, and volume:
m = ρ * V
Rearranging the equation, we get:
V = m / ρ
Substituting the given values, we have:
V = 55.0 kg / 1000 kg/m^3 = 0.055 m^3
Now, let's find the displacement while decelerating in the water. We can use Newton's second law of motion:
F_net = m * a
Where:
F_net is the net force
m is the mass of the diver
a is the acceleration
Rearranging the equation, we have:
a = F_net / m
Substituting the given values, we have:
a = 1480 N / 55.0 kg = 26.909 m/s^2
Now, let's find the time taken to reach a velocity of zero in the water using the equation:
v = u + at
Where:
v is the final velocity (which is zero since the diver comes to rest)
u is the initial velocity (which is zero)
a is the acceleration (-26.909 m/s^2)
t is the time
Rearranging the equation, we have:
t = -u / a
Substituting the given values, we have:
t = -0 / (-26.909) = 0 seconds
This means that the diver comes to rest in the water instantaneously.
Finally, the total distance traveled is the sum of the distance traveled while falling freely (0 meters) and the distance traveled while decelerating in the water (5.6 meters).
Total distance = 0 + 5.6 = 5.6 meters
Therefore, the total distance between the diving board and the diver's stopping point underwater is 5.6 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 travels in the air and the distance the diver travels in the water.
First, let's calculate the distance the diver travels in the air. We can use the kinematic equation:
s = ut + (1/2)at^2
where:
s = distance
u = initial velocity (0 m/s as the diver is at rest before stepping off the diving board)
a = acceleration (due to gravity, approximately 9.8 m/s^2)
t = time
We need to find the time it takes for the diver to reach the water's surface. We can use the equation:
v = u + at
where:
v = final velocity (0 m/s as the diver comes to rest)
u = initial velocity
a = acceleration (due to gravity)
Rearranging the equation, we have:
t = (v - u) / a
Plugging in the values:
t = (0 - 0) / 9.8
t = 0 s
Since the time is 0 s, the diver drops instantaneously from the diving board to the water's surface. Therefore, the distance traveled in the air is 0 m.
Next, let's calculate the distance the diver travels in the water. We can use the equation:
s = ut + (1/2)at^2
where:
s = distance (5.6 m)
u = initial velocity (0 m/s as the diver is at rest before reaching the water's surface)
a = acceleration (provided by the water, 1480 N / 55 kg ≈ 26.91 m/s^2)
t = time
Rearranging the equation, we have:
t^2 = (2s) / a
Plugging in the values:
t^2 = (2 * 5.6) / 26.91
t^2 = 0.2091
t ≈ 0.457 s
Therefore, the diver travels for approximately 0.457 seconds in the water.
Finally, we can find the total distance by adding the distance traveled in the air (0 m) and the distance traveled in the water (5.6 m):
Total distance = Distance in air + Distance in water
Total distance = 0 m + 5.6 m
Total distance = 5.6 m
Hence, the total distance between the diving board and the diver's stopping point underwater is 5.6 meters.
The energy the diver had when hitting the water has to equal the upward force and distance in the water.
mgh=force*distance
h= force*distance/mg=1480*5.6/(55*9.8) meters.