Two bumper cars in a circular ride area (assume it is frictionless) that has a d

Question

Two bumper cars in a circular ride area (assume it is frictionless) that has a diameter of 60 m and collide in the center of the rink. Something goes wrong with the cars and instead of bumping off each other they stay together after the collision! The first car has a mass of 120 kg and was travelling north with a speed of 3.5 m/s before the collision. The second car has a mass of 140 kg and was originally heading west going 2.0 m/s.

a. How long will it take them to travel to the edge of the ride area?

b. Where will they reach the edge of the area ? Your answer should be given as an angle north of west.

Explanation / Answer

a)
Let north be positive y direction and west be negative x direction
m1 = 120 Kg
v1 = 3.5 y m/s
m2 = 140 Kg
v2 = -2 x m/s

use conservation of momentum
m1*v1i + m2*v2i = (m1+m2)*vf
120*3.5 y - 140*2 x = (120+140)*vf
420 y - 280 x = (260)*vf
vf = (1.62 y - 1.08 x ) m/s

magnitude = sqrt (1.62^2 + 1.08^2) = 1.95 m/s
angle north of west = atan (1.62/1.08) = 56.3 degree

distance to be moved = radius = 30 m
time = distance / speed
= 30 / 1.95
   = 15.4 s
     
b)
angle as we found above = 56.3 degree

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