Physics momentum problem (with batman)?

Question

I'm having trouble with this problem (especially the last part of it)

Batman(mass of 100kg) swings from a line fixed to a chandelier to kick the Joker(mass of 70 kg) who is directly under the chandeilier. if Batman swings through a height of 2.00m and has a velocity of 3.00 m/s AFTER he kicks the Joker, how far will the joker slide along the floor? Noted: take the coefficent of kinetic friction between the floor and the joker to be .400.

please help..

Answer 1

Momentum, not energy, was conserved in this collision.
Batman's speed at contact was Vo = √(2gh) = √(2*9.8*2) = 6.261 m/s. Since his speed afterward was 3.0 m/s, he transfered (6.231 -3.0)*100kg = 326.1 kg.m/sec impulse to the Joker.

Since the Joker's mass was 75 kg, he suddenly gained 326.1/75 = 4.348 m/s speed. With a frictional force of 75*9.8*.4 = 294 N, his decelleration value is d = F/m = 294/75 = 3.92 m/s².

Distance to stop is then given by x = V²/2a = 4.348²/(2*3.92) →

x = 2.41 meters

Answer 2

If batman has lost 2.00 m in distance to the ground when he kicks the Joker, he would have converted
100kg * 9.8 m/s *2.00 m = 1960 J
of potential energy into energy kinetic energy. (E = mgh)

He didn't transfer all of this energy over to the Joker when he kicked him, though. He was moving at 3.0 m/s afterwards, which means he kept
E = (1/2) * 100kg * 3.00m/s^2 = 450 J
of kinetic energy. (E = 1/2 mv^2)

So the energy he transfered to the Joker was
1960-450 = 1510 J

When the Joker slides on the ground, he experiences a frictional force
F = uN = umg,
where u is the coefficient of friction and N is the normal force given by mg, mass times acceleration due to gravity.
F = .400*70*9.8 = 274.4 N

After the Joker slides a distance d, the amount of work done on him by the frictional force is W = f*d, which is the same as the amount of energy he would loose to friction over this distance.

Since the Joker had 1510 J to start with, the amount of distance he can travel given the friction is:
d = W/f = 1510/274.4 = 5.50 m

Answer 3

The answer is in the hint itself P initial = P final The initial momentum of student and jacket is zero as they are both not moving The final momentum is the momentum of boy and jacket after he throws the jacket 0 = m1x v1 + m2 x v2 = 3 x 14 + 82 x v2 v2 = - 3 x 14 / 82 = - 0.5 m/s The negative sign shows that he moves in a direction opposite to jacket , so that the sum of his momentum and jacket's momentum is zero As there is no friction he will continue to move without loss of speed

Answer 4

until the joker hits something to make him stop like the wall, but he will probably slide about 6-10 meters