A 52.2 kg driver steps off a diving board

[mustang]

Problem 19.
given: g=9.81 m/s^2.
A 52.2 kg driver steps off a diving board and drops straight down into the water. The water provides an average net force of resistance of 1518 N to the diver's fall.
If the diver comes to rest 5.2 m below the water's surface, what is the total distance between the diving board and the diver's stopping point underwater? Answer in units of m.

Problem 11.
Given: g =9.81 m/s^2
A 2.6*10^3 kg car accelerates from rest at the top of a driveway that is sloped at an angle of 19.1 degrees with the horizontal. An average frictional force of 4.2*10^3 N impedes the car's motion so that the car's speed at the bottom of the driveway is 4.1 m/s.
What is the length of the driveway? Answer in units of m.

 

[Hurkyl]

What work have you done on these problems so far?

 

[mustang]

For problem 19 my teacher said to used
mass*gravity*height=Force*distance of the driver below the water. Which I will use to slove for the height and add the height to the distance the driver went below the water. However, when I got my answer 20.6304m and submitted it the answer was wrong.
For the other problem I don't know where to start.

 

[Hurkyl]

Do you know where that equation came from?

Your teacher used the work-energy theorem; the change in the energy of a system is equal to the work done on the system.


Here, the only energy change is gravitational potential energy (ΔU = m g Δh), and we can compute the work applied by the water as ΔW = F Δx, and setting these equal give the equation your teacher suggested.

However, note that Δh here is the displacement between the diver's initial and final positions, not the height of the diving board above the water... so Δh (aka height in your teacher's equation) is the answer you're looking for.


For problem 11, the easiest way is to use the work-energy theorem again:

ΔW = ΔU = ΔGPE + ΔKE

You can directly compute the change in kinetic energy, ΔKE, and You can figure out ΔW and ΔGPE in terms of the length of the driveway. (you will need to use trig to get a formula for the initial height in terms of the driveway's length). Once you have that, you can solve for the driveway's length.

As a word of warning, make sure you are careful about your signs! One or more of these quantites might be negative!

 

[mustang]

So for problem 19. when finding h I got 15.41471874. Is this correct?