A skater is using very low friction rollerblades. A friend throws a Frisbee at her, on the straight line along which she is coasting. Describe each of the following events as an elastic, an inelastic, or a perfectly inelastic collision between the skater and the Frisbee. Required:
a. She catches the Frisbee and holds it.
b. She tries to catch the Frisbee, but it bounces off her hands and falls to the ground in front of her.
c. She catches the Frisbee and immediately throws it back with the same speed (relative to the ground) to her friend.

a)  perfectly inelastic,  b)  collision is inelastic,  c)   elastic  

Explanation:

In this exercise, it is asked to identify what type of shock occurs between the skater and the frisbee, for this we must define a system formed by the skater and the fribee, so that the forces during the crash have been internal and the amount of movement is preserved

Initial instant. Before the skater touches the frisbee

    p₀ = M v₁ + m v₂

where M and m are the masses of the skater and frisbee, respectively

for the final moment they give us several possibilities, in all case the moment is conserved

       p₀ =

case a)

Final instant. grabs the frisbee and holds it

    p_{f} = (M + m) v '

     p₀ = p_{f}

We can see that this shock is perfectly inelastic, it holds the fressbee

case b)

final instant.

This case is similar to the previous one, but the final speed of fresbee is zero, therefore this collision is inelastic and the kinetic energy is not conserved.

case c)

final instant. Grab the fressbee and resend it

this is an elastic Shock since the equivalent of a rebound of the fressbee, the kinetic energy is conserved.

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west