Jill has just gotten out of her car in the grocery store parkinglot. The parking

Question

Jill has just gotten out of her car in the grocery store parkinglot. The parking lot is on a hill and is tilted 3o.Fifty meters downhill, an old lady lets go of a fully loadedshopping cart. The cart, with frictionless wheels, starts to rollstraight downhill. Jill immediately starts to sprint after the cartwith her top acceleration of 2.0 m/s^2. How far has the cart rolledbefore Jill catches it?

One of the biggest questions about this question is, how do I knowthe speed of something frictionless? Because there is virtually noinformation given about the cart...please help!

Explanation / Answer

Remember that objects with different masses will fall at the same rate. This means if they are sliding on frictionless surfaces or rolling on frictionless (and massless wheels) they still fall at the same rate but the acceleration will be reduced by the sine of the angle. So in this case, for the cart F = m*a=mg*sine(theta). The masses cancel. Since we know g and the angle we can find the acceleration of the cart. From there it is just plug and slug intothe standard equations of motion.

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