A 56 kg swimmer jumps off a 15 m tower. Find the swimmer's velocity when hitting the water. The swimmer comes to a stop 2 m below the surface. Find the net force exerted by the water.
In the air:
Vi=0, d=15m, a=9.8m/s^2, vf=?
vf^2=vi^2+2ad
vf^2=0^2+2*9.8*15
vf=17.15m/s --> speed when hitting the water
Now for the water part:
vi=17.15m/s, vf=0,d=2,a=?
vf^2=vi^2+2ad
0^2=17.15^2+2*a*2
a=-73.5 m/s^2
F=ma
F=56*73.5=4116 N
To find the swimmer's velocity when hitting the water, we can use the principle of conservation of energy.
First, we can calculate the potential energy of the swimmer when they jump off the tower and just before hitting the water.
The initial potential energy can be calculated using the formula:
Potential energy = mass * acceleration due to gravity * height
Potential energy before jumping off the tower = 56 kg * 9.8 m/s^2 * 15 m
When the swimmer comes to a stop 2 m below the surface, all the potential energy is converted into kinetic energy.
Therefore, kinetic energy = potential energy
Using the formula for kinetic energy, which is:
Kinetic energy = 0.5 * mass * velocity^2
We can rearrange the equation to solve for velocity:
Velocity = √(2 * kinetic energy / mass)
Substituting the values, we have:
Velocity = √(2 * (potential energy before jumping off the tower - potential energy at 2 m depth) / mass)
Let's calculate the potential energy at 2 m depth:
Potential energy at 2 m depth = mass * acceleration due to gravity * depth
= 56 kg * 9.8 m/s^2 * 2 m
Now, we can substitute the values into the equation to find the swimmer's velocity:
Velocity = √(2 * ((56 kg * 9.8 m/s^2 * 15 m) - (56 kg * 9.8 m/s^2 * 2 m)) / 56 kg)
Simplifying the equation gives:
Velocity = √(2 * 9.8 m/s^2 * (15 m - 2 m))
Velocity = √(2 * 9.8 m/s^2 * 13 m)
Velocity = √(2 * 127.4 m^2/s^2)
Velocity = √(254.8 m^2/s^2)
Velocity ≈ 15.96 m/s
Now, to find the net force exerted by the water, we can use Newton's second law of motion.
Newton's second law states that force (F) is equal to the mass (m) multiplied by the acceleration (a):
Force = mass * acceleration
The acceleration of the swimmer is given by the change in velocity divided by the time it takes for the swimmer to stop (2 m/s divided by the time it takes).
Using the equation for acceleration, we can rearrange it to solve for force:
Force = mass * (change in velocity / time)
However, since the swimmer comes to a stop and the question does not provide the time, we cannot directly calculate the net force exerted by the water based on the given information.