Please show every step. Thanks in advance! Problem 1 . A 20 kg girl is standing

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Please show every step. Thanks in advance!

Problem 1 . A 20 kg girl is standing on a plank that has a mass of 80 kg. The plank is initially at rest but LI free to slide on a frozen pond (frictionless and horizontal). The girl begins to walk at a constant velocity of 1.5 i m/s relative to the plank. (a) What is her velocity relative to the ice surface? (b) What is the velocity of the plank relative to the ice surface? Problem 2 . Pluto's diameter is approximately 2370 km and the diameter of its satellite Charon is 1250 km. Although the distance varies, they are often about 19,700 km apart, center -to -center. Assuming that both Pluto and Charon have the same density, find the location of the center of mass of this system relative to the center of Pluto. Problem 3 . Two cars (let mA = ma = 1000 kg) collide and get so mangled they stick together and slide off as one object. Use VA = 13 m/s and theta=55 degree. The speed limit was 15.6 m/s (equivalent to 35 mph). The driver of car B says he was not speeding. Determine 08 and see if he was telling the truth. Problem 4 . Two curling stones one red and one yellow are involved in an m5 v elastic, glancing collision. The yellow stone is initially at rest and is struck by the red stone moving with a speed vi. After the collision the red stone moves A along a direction that makes an angle theta with its initial direction of motion. The velocities of the two stones are perpendicular after the collision. Determine the m vg final speed of each stone.

Explanation / Answer

1)Let v be the velocity of plank relative to ice.

Conserving momentum,

0=20*(1.5-v)+80*(-v)

v=0.3m/s

Her velocity relative to ice=1.5i-0.3i=1.2i m/s

Velocity of plank relative to ice=-0.3 i m/s

2)Let M be mass of pluto

Mass of Charon=(Rc^3/Rp^3)*M=(1250/2370)^3*M=0.1467M

Distance of CoM from Pluto's centre=0.1467M*19700/(M+0.1467M)=2520km

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