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 5.2 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 28.3 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

length of the slope L = 28.3 m

sintheta = h/L

height h = L*sintheta

initial energy Ei = Ui = m*g*h

at the bottom final energy Ef = Kf = (1/2)*m*v^2

from energy conservation

Ef =Ei

(1/2)*m*v^2 = m*g*h

v = sqrt(2*g*h)

v = sqrt(2*9.8*28.3*sin5.2)

v = 7.09 m/s<<<-------------answer

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