Two ice skaters not paying attention collide in a completely inelastic collision, prior to the collision, skater 1, with a mass of 60 kg, has a velocity of 5.0 km/h eastward, and moves at a right angle to skater 2, who has a mass of 75 kg and a velocity of 7.5 km/h southward. what is the velocity (magnitude and direction) of the skaters after collision? hint: define the +x-axis by the initial velocity of skater 1 from west to east and the +y-axis by the initial velocity of skater 2 from north to south

°    

θ  is the angle that goes from the positive x axis to the positive y axis

Explanation:

The skaters collide in a completely inelastic collision, in other words they have the same velocity after the collision, this velocity has a magnitude V and an angle respect the axis X.

We need to use the conservation of momentum Law, the total momentum is the same before and after the collision.

In the axis X:

    (1)

In the axis Y:

     (2)

We solve the last equations, we divide them:

°    

θ  is the angle that goes from the positive x axis to the positive y axis

We add the squares of the equations  (1)  and (2):