Question

An object (A) of mass m = 28.5 kg is moving in a direction that makes angle of 54° south of east with a speed v = 4.85 m/s, while object (B) of mass m = 15.5 kg is moving due north with a speed v = 7.95 m/s. The two objects collide and stick together in a completely inelastic collision. Find the magnitude of the final velocity of the two-object system after the collision.

Answer 1

The magnitude of the final velocity of the two-object system after the collision is approximately 260.363 kg·m/s.

Step-by-step explanation:

In an inelastic collision, the objects stick together after the collision and move as one. To find the magnitude of the final velocity of the two-object system, we can use the principle of conservation of momentum.

First, we need to determine the initial momentum of each object. Object A has a mass of 28.5 kg and a velocity of 4.85 m/s at an angle of 54° south of east. To calculate the x and y components of its momentum, we can use the trigonometric functions:

Momentum of A in the x-direction: 28.5 kg * 4.85 m/s * cos(54°) = 128.484 kg·m/s

Momentum of A in the y-direction: 28.5 kg * 4.85 m/s * sin(54°) = 102.016 kg·m/s