Question

Jack (mass 54.0 kgkg) is sliding due east with speed 8.00 m/sm/s on the surface of a frozen pond. He collides with Jill (mass 46.0 kgkg), who is initially at rest. After the collision, Jack is traveling at 5.00 m/sm/s in a direction 34.0∘∘ north of east. Ignore friction.

What is the direction of the Jill's velocity after the collision?

What is the magnitude of the Jill's velocity after the collision?

Answer 1

Using law of conservation of momentum,

(54 x 8)i + 0 = (54 x 5 (cos(34)i + sin(34)j) + 46 v

Velocity, v = (208.16i - 150.98j)/46

v = 4.53i - 3.28j

Velocity, |v| = sqrt(4.53^2 + 3.28^2) = 6.40 m/s (Part B)

Direction, theta = arctan(-3.28/4.53) = 35.9° S of E (Part A)

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