Two bumper cars in a circular ride area assume it is frictio

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.

Solution

a)

Conserving momentum before and after collision:

120*(3.5 j) + 140*(-2 i) = (120+140)*v

where

v = final velocity of the combined mass

i = unit vector along the East direction

j = unit vector along the North direction

So, 420 j - 280 i = 260 v

So, v = -1.08 i + 1.62 j

So, speed = sqrt(1.08^2 + 1.62^2) = 1.95 m/s

So, time taken to reach edge of the ride area = 60/1.95 = 30.8 s <--------answer

b)

direction = atan(1.62/1.08) = 56.3 deg North of west