Question

A 41.0-kg child finds himself trapped on the surface of a frozen lake, 10.0 m from the shore. The child slips with each step on the frictionless ice and remains the same distance from the shoreline. Egged on by his parents, he throws a 0.300-kg ball he is carrying toward the center of the lake with a horizontal speed of 2.00 m/s, in the direction opposite that of the shoreline. (The speed of the ball is relative to the lake.)

(a) Does the act of throwing the ball cause the child to move? If so, what are the speed and the direction of his motion with respect to the Earth?

(b) What are the forces acting on the child when he throws the ball?
the child pushing on the ball,

the force of gravity, the normal force from the ice,

the ball pushing back on the child

Answer 1

a] Yes, it causes the child to move as by momentum conservation momenta of both ball plus child must be zero. So if ball is moving towards center of lake, child should move toward shoreline.

mv + MV = 0 where m,v are mass and velocity if ball, M,V are mass and velocity of child.

V = mv/M = 0.3*2/41 = 0.0146 m/s answer

direction = towards the shoreline

b] Following forces are acting:

the force of gravity,

the normal force from the ice,

the ball pushing back on the child