Kelly is driving a car with a mass of 800 kilograms in a south direction with a speed of 18 meters/second. Dominic is driving a truck with a mass of 1500 kilograms with a velocity of 15 meters/second to the east. They undergo perfectly inelastic collision. What is the magnitude of the final momentum of both the truck and the car.

We are given

m1 = 800 kg

v1 = 18 m/s south

m2 = 1500 kg

v2 = 15 m/s east

Using the momentum balance for perfectly inelastic collision

Along the x:

m1v1 + m2v2 = (m1 + m2) vx

0 + 1500 (15) = (800 + 1500) vx

vx = 9.78 m/s

Along the y:

800 (-18) + 0 = (m1 + m2) vy

vy = - 6.26 m/s

The magnitude is

v = √ (vx² + vy²)

v = √ (9.78² + (-6.26) ²)

v = 11.61 m/s