Question

A 1550 kg car moving south at 12 m/s with a 2550kg van moving west. The vehicles stick together and move at 36 degrees south of west after the collision. Calculate (a) the initial velocity of the 2550 kg van and (b) the final velocity of the car and van. Please include a picture/diagram with your work.

Answer 1

We can consider the conservation of linear momentum in the south direction.
M_C v_S = M V sin 36
Where M_c is the mass of the car, v_s is the velocity along the south direction of the car, M is the combined mass of the car and the van and V is the final velocity of the combined system.
1550 kg x 12 m/s = (1550 + 2550) V sin 36
V =  7.72 m/s
a) The initial velocity of the van can be found from the momentum conservation along the west direction.
M_V v_W =  M V cos 36
We need to find v_w , the velocity of the van.
2550 kg x v_w =  (1550 + 2550) x 7.72 x cos 36
v_w =  10.04 m/s
The initial velocity of the van is 10.04 m/s
b) The final velocity of the car and van is found to be
V = 7.72 m/s