Two Dimensional Physics Inelastic Collision

Question

If a 1722 kg car, moving at 8 m/s north, hits and sticks to a 2149 kg truck, moving at 7 m/s west, find the direction of the final speed.

Answer 1

We use the conservation of momentum to solve this type of problem. For an inelastic collision:

m₁v₁ + m₂v₂ = (m₁ + m₂)v_f

Using the above equation we can find the total momentum in the horizontal (x) and vertical (y) directions

For the x direction:

m₁v₁ + m₂v₂ = (m₁ + m₂)v_f

0 + 2149 (-7) = (1722 + 2149)V_fx

-15043 = 3871 V_fx

-3.89 = V_fx

So the final velocity of the collision in the x direction is 3.89 ^m/_s to the west

For the y direction

m₁v₁ + m₂v₂ = (m₁ + m₂)v_f

1722 * 8 + 0 = (1722 + 2149) V_fy

13776 = 3871 V_fy

3.56 ^m/_s = V_fy

The final velocity of the collision in the y direction is 3.56 ^m/_s to the north

The magnitude of the final velocity is:

V_f = √ (V_fx² + V_fy²)

= √(-3.89² + 3.56²

= 5.27 ^m/_s

The direction is

tan θ = ¹³⁷⁷⁶/₁₅₀₄₃

θ = 42.48°

Which would be 42.48° north of west.