Two 75.0 kg hockey players skating at 5.60 m/s collide and stick together. If the angle between their initial directions was 115°, what is their velocity after the collision? (Let the motion of player 1 be in the positive x-direction and the motion of player 2 be at an angle of 115° measured counterclockwise from the positive x-axis.)
To solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision should be equal to the total momentum after the collision.
Let's break down the initial velocities of the players into their x and y components.
For player 1:
Initial velocity in the x-direction (V1x1) = 5.60 m/s
Initial velocity in the y-direction (V1y1) = 0 m/s (since it's in the positive x-direction)
For player 2:
Initial velocity in the x-direction (V1x2) = 5.60 m/s * cos(115°) (because the angle is measured counterclockwise from the positive x-axis)
Initial velocity in the y-direction (V1y2) = 5.60 m/s * sin(115°) (because the angle is measured counterclockwise from the positive x-axis)
Now, let's calculate the initial momentum (P1) using the mass (m1) and the initial velocities (V1x1 and V1y1) of player 1, and the same for player 2 (m2, V1x2, and V1y2).
P1 = m1 * V1x1 + m2 * V1x2 for the x-direction
P2 = m1 * V1y1 + m2 * V1y2 for the y-direction
Since the players stick together after the collision, their final velocity (V2) will have an x-component (V1x2) and a y-component (V1y2).
Now, let's calculate the final momentum (P2) using the same mass for both players (m) and the final velocity (V2) in the x- and y-directions.
P2 = 2 * m * V2x for the x-direction
P2 = 2 * m * V2y for the y-direction
Since the total momentum should be conserved, we have:
P1 = P2
m1 * V1x1 + m2 * V1x2 = 2 * m * V2x for the x-direction
m1 * V1y1 + m2 * V1y2 = 2 * m * V2y for the y-direction
Now, you can substitute the given values for the mass, initial velocities, and the angle to solve for V2x and V2y. The magnitude of the final velocity can be found using the Pythagorean theorem:
Magnitude of the final velocity (V2) = sqrt(V2x^2 + V2y^2)
I hope this explanation helps you understand how to approach this problem!
Your teacher made this very simple. Notice that the momentum of each is the same, which means the final momentum will be along the angle bisector of the oriainal angle separation.
So each is 115/2 off that final path.
final momentum=2*75*5.60*cos(115/5)=2*75*
V
solve for V