- #1

dwdoyle8854

- 16

- 0

## Homework Statement

A 40kg girl and an 8.4 kg sled are on the frictionless ice of afrozen lake, 15m apart but connected by a rope of negligible mass. The girl exerts a horizontal 5.2 N force on the rope. Whatare the aceleration magnitudes of a) the sled and b) the girl? c) How far from the firls initial position do they meet?

## Homework Equations

f = ma

Δx=V

_{0}t + 1/2 at

^{2}

## The Attempt at a Solution

So this is easy enough until part c) where the solution manual and I disagree.

The solution manual states "The accelerations of the sled and girl are in opposite directions."

and i just can't imagine why.

In parts a) and b) i find the magnitudes of the accelerations for the girl and sled respectively to be

0.62 m/s

^{2}= a

_{sled}

0.13 m/s

^{2}= a

_{girl}

to solve for when the collision i guess happens i set

x

_{final, girl}=x

_{final, sled}

and solving for time:

t=√( (2x

_{0, girl}/(a

_{sled}- a

_{girl}) )

the solution manual however has:

t=√( (2x

_{0, girl}/(a

_{sled}+ a

_{girl}) )

which is because they state the girl is accelerating in the opposite direction of the sled.

But the girl is pulling on the sled, and everything is frictionless. How could she be accelerating in the opposite direction of the sled if she is pulling it?

freebody diagram of girl, x-axis

<--5.2N--()--5.2N--> by Newtons 3rd law.