Two shuffleboard disks of equal mass, one orange and the other yellow, are invol

Question

Two shuffleboard disks of equal mass, one orange and the other yellow, are involved in an elastic, glancing collision. The yellow disk is initially at rest and is struck by the orange disk moving with a speed of 4.40 m/s. After the collision, the orange disk moves along a direction that makes an angle of 35.0 degrees with its initial direction of motion. The velocities of the two disks are perpendicular after the collision. Determine the final speed of each disk.

orange disk: __ m/s

yellow disk: __ m/s

Explanation / Answer

Call them v1, velocity of the striking disk, and v2, velocity of the disk originally at rest. Since the angle between them is 90 degrees, and v1 is at 37 degrees to the original direction, v2 must be at 53 degrees to the original direction of disk 1.So then, let's go:

v1 cos37 + v2 cos53 = 5 m/s .......... 1)
v1 sin37 - v2 sin53 = 0 .................... 2)

Solve the linear system to get v1 and v2. Suggestion for quick solving: multiply 1) by sin53 and 2 by cos53 and add to get an expression for v1 that is simple to evaluate, and use a similar method for v2.

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