Question

A blue car with mass m_c = 537 kg is moving east with a speed of v_c = 20 m/s and collides with a purple truck with mass m_t = 1380 kg that is moving south with an unknown speed. The two collide and lock together after the collision moving at an angle of θ = 56° South of East1)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?

Answer 1

given,

mc = 537 kg

vc = 20 m/s

mt = 1380 kg

theta = 56 degree

initial horizontal momentum = 537 * 20

initial horizontal momentum = 10740 kg.m/s

initial momentum of car = 10740 kg.m/s

final horizontal momentum = (537 + 1380) * v_x

by conservation of momentum

initial momentum = final momentum

10740 = (537 + 1380) * v_x

v_x = 5.6 m/s

final velocity * cos(56) = v_x

final velocity * cos(56) = 5.6

final velocity = 10.01 m/s

vertical momentums

1380 * v = (1380 + 537) * 10.01 * sin(56)

v = 11.527 m/s

speed of truck before collision = 11.527 m/s

initial momentum of truck = 1380 * 11.527

initial momentum of truck =15907.26 kg.m/s

magnitude of the momentum of the car-truck combination immediately after the collision = (1380 + 537) * 10.01

magnitude of the momentum of the car-truck combination immediately after the collision = 19189.17 kgm/s

speed of the car-truck combination immediately after the collision = 10.01 m/s