Quick Phys question before test, involves Energy, just confused? Help please

[jcfor3ver]

Homework Statement

The rope of a swing is 2.90 m long. Calculate the angle from the vertical at which a 81.0 kg man must begin to swing in order to have the same KE at the bottom as a 1450 kg car moving at 1.05 m/s (2.35 mph).

Homework Equations

KE=1/2mv^2
PE=mgh
SOH CAH TOA (trig reference)

The Attempt at a Solution

I made a right traingle from the mass at the beginning of its journey to the very bottom (middle of the rope). Then I found the KE at the bottom which is the KE of the car. Then I took 1/2mv^2 and set it equal to the KE of the car so I could find the velocity of the man.
Then I found the height of the starting position of the man to get his gravitational PE by setting mgh=to the KE of the car to find h.

What do I do after this? I am confused on how to find this optimal angle.

 

[p21bass]

Homework Statement

The Attempt at a Solution

I made a right traingle from the mass at the beginning of its journey to the very bottom (middle of the rope). Then I found the KE at the bottom which is the KE of the car.

I don't understand what you mean here. But it sounds like you did everything else correctly, so far. If you know the length of the rope, and how high he starts, you then can subtract how high he is from the rope length and solve for the angle by trig.

What did you get for starting height?

 

[Adjuster]

You are asked to find the initial angle for the swing. Assuming the swing has negligible losses, the man's PE at this point will be the same as his KE at the bottom.

You can therefore work out how high the man must be raised at the start so that his PE is equal to the car's KE, and use the rope length and trigonometry to find the angle.