simple physics question?

Question

An adult exerts a horizontal force on a swing to raise a child a height h above the lowest point of the cycle.

a)What is the horizontal force that the adult exerts?
b) What is the speed of the child at the bottom of the cycle?
c) What is the tension in the rope (use m,L,g)
d) If the child jumps straight off (horizontally) at the bottom of the cycle where will the child land(Assume L = 2m, h= .5 meters and the height above the ground at the lowest point is .5 meters).

Answer 1

If you assume the system is frictionless, then you can answer b, c, and d, but part a is nonsense.

The adult can supply any amount of force and get the same result (assuming no friction) as long as smaller forces are applied for longer periods of time.

In all, the adult has to supply enough energy to get the child (i.e. mass m) up a height h against the force of gravity. Hence the adult has to do the work equal to mhg.

Part b assumes that all the potential energy the child had at height h (i.e. mgh) is converted to kinetic energy (1/2)(mv^2) so you can compute v in terms of g and h.

Part c uses the centripetal acceleration: the force of gravity down subtracted from the tension up should equal the centripetal force required by the velocity (from part b) and the length of the swing (I assume that's what L is supposed to be) which is the radius of the circle.

Part d is classic ballistic motion. How long does it take for the child to hit the ground (depends on the size of the child, but I think this wants the child to be of size 0)? How far horizontally does the child move in that time?