Question

A blue car with mass m_c = 497 kg is moving east with a speed of v_c = 16 m/s and collides with a purple truck with mass m_t = 1336 kg that is moving south with an unknown speed. The two collide and lock together after the collision moving at an angle of θ = 51° South of East

1)

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

kg-m/s

2)

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

kg-m/s

3)

What is the speed of the truck before the collision?

m/s

4)

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

kg-m/s

5)

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

m/s

6)

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

Answer 1

Mass of car, m = 497
Consider M as the mass of truck
Initial velocity of car, Uc = 16
Consider Ut as the initial velocity of truck.
Consider the velocity of the truck and car after collision as V.

Using conservation of momentum along x-axis (east direction)
mUc = (m+M) V cos
V = (mUc) / [(m+M) cos]
= (497 * 16) / [(497 + 1336) * cos(51)]
= 6.89 m/s

Using conservation of momentum along y-axis (south direction)
MUt = (m+M) V sin
Ut = [(m+M) V sin] / M
= [(497 + 1336) x 6.89 x sin(51)] / 1336
= 7.35 m/s
-----------------------------------------------------
1)
Initial momentum of the car = mUc
= 497 * 16
= 7952 kg m/s

2)
Initial momentum of the truck = MUt
= 1336 * 7.35
= 9819.9 kg m/s

3)
Speed of truck before collision = Ut = 7.35 m/s

4)
Magnitude of initial momentum = SQRT[(mUc)² + (mUt)²]
= SQRT[(7952)² + (9819.9)²]
= 12635.9 kgm/s

5)
Speed of the truck-car combination = V
= 6.89 m/s

6)
Momentum of the system after collision = (m + M) V
= 12635.9 kg m/s
Momentum before collision = Momentum after collision