A blue car with mass mc = 456 kg is moving east with a speed of vc = 21 m/s and

Question

A blue car with mass mc = 456 kg is moving east with a speed of vc = 21 m/s and collides with a purple truck with mass mt = 1346 kg that is moving south with an unknown speed. The two collide and lock together after the collision moving at an angle of ? = 52° South of East.

1) What is the magnitude of the initial momentum of the car?

2) What is the magnitude of the initial momentum of the truck?

3) What is the speed of the truck before the collision?

4) What is the magnitude of the momentum of the car-truck combination immediately after the collision?

5) What is the speed of the car-truck combination immediately after the collision?

6) Compare the magnitude of the TOTAL momentum of the system before and after the collision:

Explanation / Answer

Let v is the speed of both vehicles after collision.

in x-direction

m1*v1x = (m1+m2)*vx

m1*v1x = (m1+m2)*v*cos(52)

v = m1*v1x/( (m1+m2)*cos(52))

v = 456*21/( (456+1346)*cos(52))

v = 8.63 m/s

1) What is the magnitude of the initial momentum of the car?

pc = mc vc = 456.0 * 21.0 = 9576 Kg.m/s

2) What is the magnitude of the initial momentum of the truck?

in y -direction

initai momentum of truck
pt = m2*v2 = (m1+m2)*v*sin(52)

= (456+1346)*8.63*sin(52)

= 12254.5 kg.m/s

3)

spedd of truck before collision,
v2 = pt/mt = 12254.5/1346 = 9.10 m/s

4) What is the magnitude of the momentum of the car-truck combination immediately after the collision?

?(95762+12254.52) = 15552.2 Kg.m/s

5) What is the speed of the car-truck combination immediately after the collision?

15552.2 /(456+1346) = 8.63 m/s

6) Compare the initial and final kinetic energy of the total system before and after the collision:

before:

0.5*456*21*31 + 0.5*1346*9.10*9.10 = 204159.1 J

after:

0.5 * (456+1346) * 8.63*8.63 = 67103.6 J

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