Answer to Question #144330 in Mechanics | Relativity for rsw

Question

A person is trying to run away up a slippery hill. The only thing limiting her acceleration is friction. If the hill is (d) meters long and she is starting from standing at the bottom, how much time will it take her to get to the top? Find time in terms of coefficient of friction (u), the angle of the hill (theta), length of the hill (d) and (g).

Answer 1

Since acceleration limits the friction force, the traction force is equal to the friction force $a\times m = m\times g\times\cos {\theta }\times\mu$ ;

Because $a =\frac {2\times S} {t ^ 2}$ then

$t=\sqrt{\frac{2\times d}{\cos{\theta}\times \mu \times g}}$