Question

ill has just gotten out of her car in the grocery store parking lot. The parking lot is on a hill and is tilted 3 degrees. Fifty meters downhill from Jill, a little old lady lets go of a fully loaded shopping cart. The cart, with frictionless wheels, starts to roll straight downhill. Jill immediately starts to sprint after the cart with her top acceleration of 2.0m/s2.How far has the cart rolled before Jill catches it?

Answer 1

Answer:

$t=25.6446\ s$

is the time after which Jill will be able to catch the cart.

Explanation:

Given:

• angle of inclination, $\theta=3\ ^{\circ}$

• height of the cart from the level ground, $h=50\ m$

• acceleration of Jill, $a=2\ m.s^{-2}$

Now the component of gravity acting on the cart along the inclined plane:

$g'=g.sin\ \theta$

$g'=9.8\times sin\ 3^{\circ}$

$g'=0.5129\ m.s^{-2}$

Time taken by Jill to reach this speed:

$v=u+a.t$

where:

t = time taken

u = initial velocity = 0

$51.289=0+2\times t$

$t=25.6446\ s$ is the time after which Jill will be able to catch the cart.