Two ice skaters collide on the ice. a 39.6-kg skater moving south at 6.21 m/s collides with a 52.1-kg skater moving east at 4.33 m/s. the two skaters entangle and move together across the ice. determine the magnitude and direction of their post-collision velocity.

V = 3.6385 m/s

θ = 47.46 degrees

Explanation:

the important data in the question is:

Skater 1:

= 39.6 kg

direction: south (axis y)

= 6.21 m/s

Skater 2:

= 52.1 kg

direction: east (axis x)

= 4.33 m/s

Now using the law of the conservation of linear momentum ( and knowing that the collision is inelastic we can do the next equations:

 (eq. 1)

 (eq. 2)

Where and is the velocity of the sistem in x and y after the collision.

Note: the conservation of the linear momentum have to be make once by each axis.

Now, in the (eq. 1) the skater 1 don't have velocity in the axis x, so we can replace by 0 in the equation and get:

 (eq. 1)

also, in the (eq. 2) the skater 2 don't have velocity in the axis y, so we can replace by 0 in the equation and get:

 (eq. 2)

Now, we just replace the data in both equations:

 (eq. 1)

 (eq. 2)

solving for and we have:

= 2.46 m/s

= 2.681 m/s

using the pythagoras theorem we can find the magnitude of the velocity as:

V =

V = 3.6385 m/s

For find the direction we just need to do this;

θ =

θ = 47.46 degrees