1. Two skaters collide and embrace. One, whose mass is 70 kg, is initally moving

Question

1. Two skaters collide and embrace. One, whose mass is 70 kg, is initally moving east at a speed of 6.0 km/h. The other, whose mass is 50 kg, is initially moving north at a speed of 8.0 km/h. What is the final velocity of the couple (in m/s), and what fraction of the inital kinectic energy of the skaters is lost in the collision?

2. Any oxygen molecule (mass = 5.36 * 10-26kg) with an initial speed of 3.0 * 105m/s collides elastically with a hydrogen molecule (mass = 3.35 * 10-27kg), which is initally at rest. After the collision, the hydrogen moelcule moves off at an angle of 30 degrees to its initial direction. Find the speed of each molecule after the collision and the angle made with the incident direction by the recoiling target molecule.

Please briefly explain your steps for both problems. Thank you!

Explanation / Answer

a) px = m*vx = 70kg*6km/h*(1000m/km*1hr/3600s) = 135.8kg-m/s

b) py = m*vy = 50kg*8km/h*(1000m/km*1hr/3600s) =111kg-m/s

c) ? = arctan (py/px) = arctan(111/135.8) = 39.26o

d) Vx = px/(m1 + m2) = 135.8/(120) =1.313 m/s

and Vy = py/120 = 111/120 = 0.925 m/s

so V = sqrt(vx^2 + vy^2) = sqrt(1.313^2 + 0.925^2) = 1.606m/s

Ki = 1/2*m1*v1^2 + 1/2*m2*v2^2 = 220J

Kf = 1/2*(m1 + m2)*V^2 = 154J
so (220 - 154) 220 = 0.3

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