The game is called Ice Bocci. You play by sliding pucks across the ice into each other, sort of like marbles. One player slides the red puck straight into a stationary green puck. The red puck is sliding with a speed of 4 m/s and weighs twice as much as the green puck. What is the speed of the green puck after the elastic collision?
To determine the speed of the green puck after the elastic collision, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
The momentum of an object is given by the product of its mass and velocity. In this case, let's assume the mass of the red puck is M and the mass of the green puck is m.
Before the collision, the momentum of the red puck is given by the product of its mass and velocity:
Momentum of red puck before collision = Mass of red puck * Velocity of red puck
= M * 4 m/s
The momentum of the green puck is zero since it is stationary.
Total momentum before collision = Momentum of red puck before collision + Momentum of green puck before collision
= M * 4 m/s + 0
According to the principle of conservation of momentum, the total momentum after the collision will be the same as the total momentum before the collision.
Total momentum after collision = Momentum of red puck after collision + Momentum of green puck after collision
Let's assume the velocity of the green puck after the collision is v (m/s).
Momentum of red puck after collision = Mass of red puck * Velocity of red puck after collision
= M * (-v) [negative sign since the red puck changes direction]
Momentum of green puck after collision = Mass of green puck * Velocity of green puck after collision
= m * v
Total momentum after collision = Momentum of red puck after collision + Momentum of green puck after collision
= M * (-v) + m * v
We can set up the equation:
Total momentum before collision = Total momentum after collision
M * 4 m/s = M * (-v) + m * v
Simplifying the equation:
4M = (-v)M + mv
We know that the red puck weighs twice as much as the green puck, so we can substitute M = 2m into the equation:
4(2m) = (-v)(2m) + mv
8m = -2mv + mv
8m = -mv
Dividing both sides of the equation by m (assuming m is non-zero), we get:
8 = -v
Thus, the velocity of the green puck after the elastic collision is -8 m/s.