# 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.

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#### Hurkyl

Staff Emeritus
Gold Member
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

Staff Emeritus
Gold Member
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 (&Delta;U = m g &Delta;h), and we can compute the work applied by the water as &Delta;W = F &Delta;x, and setting these equal give the equation your teacher suggested.

However, note that &Delta;h here is the displacement between the diver's initial and final positions, not the height of the diving board above the water... so &Delta;h (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:

&Delta;W = &Delta;U = &Delta;GPE + &Delta;KE

You can directly compute the change in kinetic energy, &Delta;KE, and You can figure out &Delta;W and &Delta;GPE 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?

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