Answer to Question #238775 in Physics for bia

Question

Mary is standing at the top of a hill admiring the view. The hill is at a 2.90° tilt. 29.0 m down the hill an old man lets go of a stroller with a baby inside it. The stroller starts to roll downhill with its frictionless wheels. Mary starts to run after it with her best acceleration of 2.90 m/s². How far has the stroller rolled before she catches it.

Answer 1

On the one hand, the distance Mary should run to catch the stroller:

$$D=\frac{a_MT^2}2.$$

On the other hand, it is the distance the stroller covered plus x = 29 meters:

$$D=d+x,\\\space\\ d=\frac{a_sT^2}2=\frac{gT^2\sin\theta}2 ,\\\space\\ D=\frac{gT^2\sin\theta}2 +x.$$

Equate D and find the time:

$$\frac{a_MT^2}2=\frac{gT^2\sin\theta}2+x,\\\space\\ T^2=\frac{2x}{a_M-g\sin\theta}.$$

Therefore:

$$D=\frac{xa_M}{a_M-g\sin\theta}=35\text{ m}.$$