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 3.0 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 19 meters downhill from you car? Assume the only acceleration the cart feels is due to gravity down the slope (friction from squeeky wheels can be neglected).

Give your answer in m/s to three significant figures. DO NOT INCLUDE UNITS in you answer.

Explanation / Answer

jill goes 50 + x cart goes x acceleration of cart = gsin3degrees a 50 + x =1/2 (2) t^2 for jill and x = 1/2 a t^2 so (50 +x) over x = 2/a 2x = 50a + xa x(2-a) = 50a x = 50a over (2-a) since a = 9.8 sin3 = 0.51 m/s^2 x = (50)(0.51)/1.49 = 17.1 m in 8.2 s you are just about right. Maybe rounding or using g = 9.8 explains the difference.

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