Question

# A blue car with mass mc = 539 kg is moving east with a speed of...

A blue car with mass mc = 539 kg is moving east with a speed of vc = 15 m/s and collides with a purple truck with mass mt = 1300 kg that is moving south with an unknown speed. The two collide and lock together after the collision moving at an angle of ? = 52

mc = 539 kg

mt = 1300 kg

Vcxi = 15 m/s = initial velocity of car in X-direction (east)      going east.

Vtxi= initial velocity of truck in X-direction (east) = 0

Vcyi = initial velocity of car in Y-direction (south) = 0

Vtyi = initial velocity of truck in Y-direction (south)?

V = final velocity

Vfx = final velocity along X-direction = V Cos52

Vfy= final velocity along Y-direction = V Sin52

1) initial momentum of car = mc Vcxi = 539 x 15 = 8085 kgm/s

2) using conservation of momentum along the x-direction ::

mc Vcxi + mt Vtxi = (mc + mt) Vfx

539 x 15 + 1300 x 0 = (539 + 1300) V cos52

8085 = 1132.2 V

V = 7.14 m/s

So Vfy= V sin52 = 7.14 Sin52 = 5.63 m/s

using conservation of momentum along the y-direction ::

mc Vcyi + mt Vtyi = (mc + mt) Vfy

539 x 0 + 1300 x Vtyi = (539 + 1300) (5.63 m/s)

Vtyi = 7.96 m/s

initial momentum of truck = mt Vtyi= 1300 x 7.96 = 10348 kgm/s

3) speed of truck before collision = Vtyi = 7.96 m/s

4) final momentum of combination = (mc + mt) V = (1300 + 539) 7.14 = 13130.5 kgm/s

5) V = 7.14 m/s

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