Maggie and Evie are playing their favorite game in the living room - Chases and

Question

Maggie and Evie are playing their favorite game in the living room - Chases and Pounces. Maggie (m_M = 4.2 kg) is running across the floor at a speed of 3 m/s. Evie (m_E = 3.6 kg) is chasing Maggie, running diagonally at a speed of 4 m/s with the angle theta = 25 degree shown in the figure. When they arrive at the same location, there's some grappling and wrestling, and the two of them slide along the ground as a single ball of cats. What is the velocity (magnitude and direction, relative to Maggie's initial direction of travel) of the ball of cats after their collision? The floor can be considered to be frictionless due to the combination of wood floors and cat claws, and the additional speed from pouncing can be considered negligible compared to their initial speeds. After sliding on the frictionless wood for a second, the two encounter an area rug, which adds a coefficient of friction of mu_k = 0.2. How far do the cats slide before coming to rest?

Explanation / Answer

mass of maggie,mm=4.2 kg

mass of Evie,me=3.6 kg

Total mass,M=7.8 kg

Maggie velocity,vm=3 m/s

Evie velocity,Ve=4*cos25=3.62 m/s

So the velocity after collision is, vc=mmVm+meVe/ M

=4.2*3+3.62*3.6/7.8=3.288 m/s

b

Stopping distance,d=v2/2* mu g

mu=0.2

d=3.2882/(2*0.2*9.8)=2.7588 m

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