A high diver of mass 70 kg jumps off a diving board and enters the water with the speed of 10 m/s the average upward resistance force of water exerts on the diver is 200 N. How far in the water will the diver travel before coming to rest?
assume hydrostatics is negligible
F = m a
a = 200/70 = 2.86
v = Vi - a t
0 = 10 - 2.86 t
t = 3.5 seconds to stop
d = Vi t - (1/2)(2.86) t^2
d = 10 (3.5) - 1.43 (3.5)^2
d = 35 - 17.5
d = 17.5 meters
well, that is what we get. It is ridiculously high but so be it. Let's hope it is a really, really, deep pool :)
To determine the distance the diver will travel in the water, we can use the principle of work and energy.
The work done by the upward resistance force can be calculated as the force multiplied by the distance traveled:
Work = Force × Distance
In this case, the work done by the resistance force will be equal to the change in the diver's kinetic energy:
Work = Change in kinetic energy
The initial kinetic energy of the diver can be calculated using the formula:
Kinetic energy = 0.5 × mass × velocity^2
The final kinetic energy of the diver will be zero since the diver comes to rest. Therefore, the change in kinetic energy will be equal to the initial kinetic energy:
Change in kinetic energy = Initial kinetic energy
Substituting the values into the equation, we get:
Force × Distance = 0.5 × mass × velocity^2
Solving for distance:
Distance = (0.5 × mass × velocity^2) / Force
Plugging in the given values:
Distance = (0.5 × 70 kg × (10 m/s)^2) / 200 N
Calculating this equation gives the distance traveled by the diver in the water.
To determine the distance the diver will travel before coming to rest, we need to apply the principle of work and energy.
1. First, let's find the gravitational potential energy (GPE) and the kinetic energy (KE) when the diver enters the water. The formula for GPE is given by:
GPE = m * g * h
where m is the mass of the diver (70 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the height of the diving board.
2. Since the diver jumps off the diving board, we can assume that the initial GPE is converted entirely to KE. Therefore, we have:
GPE = KE
3. The formula for KE is given by:
KE = (1/2) * m * v^2
where m is the mass of the diver (70 kg) and v is the speed of the diver (10 m/s).
4. Setting GPE equal to KE:
m * g * h = (1/2) * m * v^2
5. We can rearrange the equation to solve for the height h:
h = (v^2) / (2 * g)
Using the given values, we substitute them into the equation:
h = (10^2) / (2 * 9.8) = 5.10204 m
6. Now that we have the height, the distance traveled in water before coming to rest can be found using the work-energy principle. The work done by the upward resistance force of the water is given by:
Work = Force * Distance
Since the average upward resistance force is 200 N, we need to find the distance traveled.
7. The formula for work is also given by:
Work = KE
8. Setting the work done by the upward resistance force equal to the kinetic energy:
Force * Distance = (1/2) * m * v^2
Substituting the given values:
200 N * Distance = (1/2) * 70 kg * (10 m/s)^2
9. Solving for Distance:
Distance = ((1/2) * 70 kg * (10 m/s)^2) / 200 N
10. Evaluating the equation gives:
Distance = 17.5 m
Therefore, the diver will travel a distance of 17.5 meters in the water before coming to rest.