posted by Ana on .
Two shuffleboard disks of equal mass, one orange and the other yellow, are involved in a perfectly elastic glancing collision. The yellow disk is initially at rest and is struck by the orange disk moving initially to the right at 5.60 m/s. After the collision, the orange disk moves in a direction that makes an angle of 33.4° with its initial direction. Meanwhile, the velocity vector of the yellow disk is perpendicular to the postcollision velocity vector of the orange disk. Determine the speed of each disk after the collision.
smaller speed______ m/s
larger speed_______ m/s
So far this is wut i tried,
Vo*cos33.4° + Vy*33.4° = 5.60
Vo*sin33.4° = Vy*33.4°
i don't if this make senses...i'm lost
You would ordinarily need to use both momentum and kinetic energy conservation to solve this problem, but they have told you the directions of both discs, so you have only two unknowns and can use two momentum-related equations. One of your two equations is not quite correct.
If Vo is the orange velocity after collision and Vy is the yellow velocity,
Vo sin 33.4 = Vy cos 33.4
5.60 = Vo cos 33.4 + Vy sin 33.4
Plug in the trig function values and solve the two linear equations.
Vo = 1.516 Vy
5.60 = 0.8348 Vo + 0.5504 Vy
5.60 = 1.8259 Vy
Vy = 3.07 m/s
Vo = 4.65 m/s
Whenever there is elastic collision in a problem like this (one mass hits another stationary mass of equal mass), the paths of the two particles are at right angles, unless motion remains in the same direction. In that case, they exchange velocities. This can easily shown using the Pythagorean theorem.