Picking someone up on skis
A skier is on a 100 m hill and wants to surprise her fiance at the base of the hill by picking them up while skiing. Both the skier and her fiance are 75 kg. She skis down the hill, picks up her fiance, and keeps skiing into another hill. How high up on the hill can they ski up before coming to a stop?
Won't I just do a conservation of energy where 75 kg*g*100m=2*75kg*g*h?
Answer
You have to be careful how you use conservation of energy because this problem has a collision. Energy is not always conserved in collisions! On the other hand, momentum is always conserved.
You can use energy to find the velocity of the skier at the bottom of the slope just before the collision, then use conservation of momentum to find the velocity of the skier + fiance combination right after the collision. Then you can try using energy again to find the maximum height they can get up the hill.
Customer support service by UserEcho
You have to be careful how you use conservation of energy because this problem has a collision. Energy is not always conserved in collisions! On the other hand, momentum is always conserved.
You can use energy to find the velocity of the skier at the bottom of the slope just before the collision, then use conservation of momentum to find the velocity of the skier + fiance combination right after the collision. Then you can try using energy again to find the maximum height they can get up the hill.