Question #102693

A stationary ball, with a mass of 0.5 kg, is struck by an identical ball moving at 60m/s . After the collision, the second ball moves 30° to the left of its original direction. The stationary ball moves 60° to the right of the moving ball’s original direction. What is the velocity of each ball after the collision?

Expert's answer

We can find the velocity of each ball after the collision from the law of conservation of momentum. Let's apply the law of conservation of momentum along the "x"- and "y"-axis:

here, "m = 0.5kg" is the mass of the first (stationary) and the second ball, respectively, "v_{1,i} = 0 \\dfrac{m}{s}" is the initial velocity of the stationary ball, "v_{2,i} = 60 \\dfrac{m}{s}" is the initial velocity of the second ball, "v_{1,f}" is the final velocity of the stationary ball, "v_{2,f}" is the final velocity of the second ball, "\\alpha = 30^{\\circ}" is the recoil angle of the first ball (which is moving to the left of the "x"-axis) and "\\theta = 60^{\\circ}" is the scattering angle of the second ball (which is moving to the right of the "x"-axis).

Then, we get:

Let's express "v_{1,f}" from the equation (4) and substitute it into the equation (3):

Then, we can find the final velocity of the first ball:

**Answer:**

"v_{1,f} = 52 \\dfrac{m}{s}."

"v_{2,f} = 29.8 \\dfrac{m}{s}."

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