Question

A 225 kg red bumper car is moving at 3.0 m/s. It hits a stationary 180 kg blue bumper car. The red and blue bumper cars combine and hit a stationary green bumper car of mass 150 kg. The red, blue, and green bumper cars all combine.

What is the final velocity of the combined bumper cars?
A .93m/s
B 1.2 m/s
C 1.7m/s
D 2.7m/s
Please Help!!!

Answer 1

Answer: B. 1.2 m/s

Step-by-step explanation:

First we would find the velocity with which red car and blue car move when they combine after first collision.

Using law of conservation of momentum,

Initial momentum = final momentum

Mass of red Car, Mr = 225 kg

Mass of blue car, Mb = 180 kg

Mass of green car, Mg = 150 kg

Initial velocity of red car, Ur = 3.0 m/s

Initial velocity of blue car, Ub = 0

Initial velocity of green car, Ug = 0

collision 1:

Mr Ur + Mb Ub = (Mr+Mb) V

where, V is the final velocity with which red and blue car moves.

225 × 3 + 0 = (225 + 180 ) V

⇒ V = 675/ 405 = 1.67 kg.m/s

collision 2:

These cars collide with the green car. Let the final velocity with which the three cars move together after collision: V'

(Mr+Mb) V + Mg Ug = (Mr+Mb+Mg) V'

675 + 0 = 555 V'

⇒V' = 1.2 m/s

Thus, the correct option is B.