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

Question

Vocaloid · Answer

F = ma
plug in 5.2N for the applied force. plugging in the sled's mass and solving for a will result in the acceleration of the sled
plugging in the girls' mass and solving for a will result in the acceleration of the girl

you can then set up the kinematic equation deltax = (1/2)at^2 for the girl  (making sure to use the girl's acceleration)
and deltax = - (1/2)at^2 + 15 for the sled (making sure to use the sled's acceleration) since it starts at 15 and accelerates in the opposite direction of the girl

the sled and the girl meet, so you can set these equal to each other and solve for t
then after that the position of the sled is 1/2at^2 where a is the girl's acceleration and t is the time from the previous step