You come out of the grocery store with a full shopping cart. You stop behind you

Question

You come out of the grocery store with a full shopping cart. You stop behind your car to get out your keys, unlock your car, and put your stuff inside. You didn't notice, but the parking lot is sloped at an angle of 5.4 degrees, so as soon as you let go the cart begins to roll. How fast is your cart rolling when it runs into the BMW parked 29.9 meters downhill from you car? Assume that friction and drag can be neglected. Give your answer in m/s to at least three significant figures. You won't be graded on the number of significant figures, this is just to avoid being counted off due to rounding.

Explanation / Answer

so the parking lot pushes at an angle of 85 degrees, .087 of that force is pushing the cart sideways. so acceleration on the cart is 9.8 * .087 = .854 m/s^2.

the time it takes the cart hit the hummer is:
29.9 = .54 * .854 t^2
t = sqrt(29.9/(.54*.854)) = 8.05 s

the speed it is moving at that time is:

v = at = .854*8.05 = 6.87 m/s

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