Can you please help me with this Physics question about runaway shopping trolleys?

A lady, let's call her Ms Smith, is on a hill with a slope of 3 degrees. 50m downhill from her, another lady lets go of her fully laden shopping trolley (with frictionless wheels) which begins to roll straight down the hill. Ms Smith immediately chases after the cart, with a top acceleration of 2m/s^2. How far has the trolley rolled before Ms Smith catches up to it?


Now, I've had a very long summer holiday and have completely forgotten all useful physics-related information, so how would I go about this problem?

AaronX2010-03-13T06:07:24Z

Favorite Answer

Assume mass of trolley is m.
Resolve weight of trolley into force parallel to plane and perpendicular to plane (in terms of m).
Ignore force perpendicular. Use force parallel to calculate acceleration of trolley (remember mass is m).
The problem is now a simple one of 2 bodies, starting 50m apart, the front one with the acceleration you calculated and the back one with acceleration 2.
Assume they meet at time t. Calculate the distance travelled for both bodies. Knowing the back one travels 50m further, calculate t, then the distance travelled.

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