A 59-kg woman contestant on a reality television show is at rest at the south en

Question

A 59-kg woman contestant on a reality television show is at rest at the south end of a horizontal 148-kg raft that is floating in crocodile-infested waters. She and the raft are initially at rest. She needs to jump from the raft to a platform that is several meters off the north end of the raft. She takes a running start. When she reaches the north end of the raft she is running at 4.9 m/s relative to the raft. At that instant, what is her velocity relative to the water? ________ m/s Bored, a boy shoots his pellet gun at a piece of cheese that sits, keeping cool for dinner guests, on a massive block of ice. On one particular shot, his 1.4 g pellet gets stuck in the cheese, causing it to slide 25 cm before coming to a stop. If the muzzle velocity of the gun is 62 m/s and the cheese has a mass of 135 g, what is the coefficient of friction between the cheese and ice? ________ A 2100 kg car traveling to the right at 26 m/s is chasing a second car of the same mass that is traveling to the right at 10 m/s. If the two cars collide and stick together, what is their speed just after the collision? ________ m/s What fraction of the initial kinetic energy of the cars is lost during this collision? _________ Where does it go? It is returned to the Universe. It is transmitted to the road. It is converted to momentum. It is transformed into heat, sound, and the deformation of the metal. No kinetic energy is lost.

Explanation / Answer

Q1.

as initially both raft and the contestant were at rest, velocity of the center of mass is zero.

as she moves towards north , the raft will move towards south

to keep the velocity of center of mass as zero.

let velocity of raft towards south is v m/s.

then velocity of the person w.r.t. water=velocity of person w.r.t. raft+velocity of raft w.r.t. water

=4.9-v

(-ve sign as raft's velocity is in opposite direction)

conserving velocity of center of mass to 0,

59*(4.9-v)-148*v=0

==>59*4.9=(59+148)*v

==>v=59*4.9/(59+148)=1.3966 m/s

so her velocity relative to water is 1.3966 m/s.

Q2. using conservation of momentum principle:

velocity of the cheese after collisionwith the bullet

=1.4*0.001*62/(1.4*0.001+0.135)

=0.63636 m/s

distance to be stopped=25 cm=0.25 m

initial velocity=0.63636 m/s

final velocity=0 m/s

then acceleration=(final velocity^2-initial velocity^2)/(2*distance)

=(0^2-0.63636^2)/(2*0.25)

=-0.80991 m/s^2

then friction coefficient=magnitude of acceleration/g

=0.80991/9.8=0.082644

Q3.

conserving momentum in the original direction of motion:

mass of first car*speed of first car+mass of second car*speed of second car

=combined mass of two cars*speed of the two cars

==>speed of two cars=(2100*26+2100*10)/(2100+2100)=18 m/s

part b:

kinetic energy lost=initial kinetic energy-final kinetic energy

=0.5*2100*26^2+0.5*2100*10^2-0.5*(2100+2100)*18^2

=134400 J

so fraction of kinetic energy lost=134400/(0.5*2100*26^2+0.5*2100*10^2)=0.16495

part c:

it gets transformed into heat, sound and defomration of metal.

fourth option is correct.

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