In a pairs skating competition the male skater (82 kg) is initially carrying his partner (68 kg). They are both moving backwards at 2.50 m/s right before he thr

Question

In a pairs skating competition the male skater (82 kg) is initially carrying his partner (68 kg). They are both
moving backwards at 2.50 m/s right before he throws his partner forward. What is the final velocity of the
male skater if his partner is thrown at 1.50 m/s (relative to the ice).
8. A 2.0 kg cart is moving north at 3.0 m/s and a 1.0 kg cart is moving south at 4.0 m/s. They collide and the
2.0 kg cart bounces back to the left at 1.0 m/s. What is the final speed and direction of the other cart?

Answer 1

I will answer the skaters problem.  For the carts problem, please clarify what "left" is.  One cart moves north.  Is left the same as west?

 

Skaters:

 

M = mass of male skater = 82 kg

m = mass of partner = 68 kg

v = their initial velocity when together = 2.50 m/s (assume they are moving in positive direction)

u = velocity of thrown partner relative to the ice = 1.50 m/s (will apply this in negative direction)

 

Assume linear momentum p is conserved.

w = final velocity of male skater

p_i = initial momentum = (M + m)v

p_f = final momentum = Mw - mu

 

p_i = p_f ⇒ (M + m)v = Mw - mu

 

w = [(M + m)v + mu] / M = [(82 + 68)(2.50) + (68)(1.50)] / (82) m/s

 

w = 5.82 m/s