What Are the Physics Behind a Girl Pulling a Sled on Ice?

[hansel13]

I'm not sure what the rules are about posting homework problems, but I just had 2 I couldn't get around too, so here's the second one...

Homework Statement

A 40 kg girl and a 8.4 kg sled are on the frictionless ice of a frozen lake, 15m apart but connected by a rope of negligible mass. The girl exerts a horizontal 5.2 N force on the rope.
What are the acceleration magnitudes of
(a) the sledge?
(b) the girl?
(c) How far from the girl's initial position do they meet?

Homework Equations

f=ma

The Attempt at a Solution

Finding the answers to part a and b were simple..
(a) a = f/m = 5.2N/8.4kg = .62 m/s²
(b) a = f/m = 5.2N/40kg = .13 m/s²
(c) I'm having problems figuring out part C.

 

[LowlyPion]

I'm not sure what the rules are about posting homework problems, but I just had 2 I couldn't get around too, so here's the second one...

Homework Statement

A 40 kg girl and a 8.4 kg sled are on the frictionless ice of a frozen lake, 15m apart but connected by a rope of negligible mass. The girl exerts a horizontal 5.2 N force on the rope.
What are the acceleration magnitudes of
(a) the sledge?
(b) the girl?
(c) How far from the girl's initial position do they meet?

Homework Equations

f=ma

The Attempt at a Solution

Finding the answers to part a and b were simple..
(a) a = f/m = 5.2N/8.4kg = .62 m/s²
(b) a = f/m = 5.2N/40kg = .13 m/s²
(c) I'm having problems figuring out part C.

Write equations for their positions
XG + XS = 15
XG = 1/2*ag*t²
XS = 1/2*as*t²

Solve noting that t² is the same when they meet

 

[hansel13]

1/2*ag*t²+1/2*as*t²= 15

t² = 15 / (1/2*ag +1/2*as)
t² = 15 / (1/2*.62 +1/2*.13)
t² = 40
t = 6.3m

That doesn't seem right, I'm lost.

 

[LowlyPion]

1/2*ag*t²+1/2*as*t²= 15

t² = 15 / (1/2*ag +1/2*as)
t² = 15 / (1/2*.62 +1/2*.13)
t² = 40
t = 6.3m

That doesn't seem right, I'm lost.

Not quite. That gives you seconds.

XG = 1/2*ag*t² = 1/2*(.13)*(6.3)² = 2.58m

 

[hansel13]

Not quite. That gives you seconds.

XG = 1/2*ag*t² = 1/2*(.13)*(6.3)² = 2.58m

ahh. Gotcha, thanks.