Two billiard balls undergo an elastic collision as shown in the figure below. Ba

Question

Two billiard balls undergo an elastic collision as shown in the figure below. Ball 1 is initially traveling along x with a speed of 18 m/s, and ball 2 is at rest. After the collision, ball 1 moves away with a speed of 9.0 m/s at an angle ? = 60°. (For the following questions, assume the mass of ball 1 is equal to the mass of ball 2.)

(a) Find the speed of ball 2 after the collision.

(b) What angle does the final velocity of ball 2 make with the x axis?

_____________° counterclockwise from the +x axis

Explanation / Answer

given,

initial velocity of ball 1 = 18 m/s

initial velocity of ball 2 = 0 m/s

final velocity of ball 1 = 9 m/s at 60 degree

by conservation of momentum

initial horizontal momentum = final horizontal momentum

m * 18 + 0 = m * 9 * cos(60) + m * v_x

v_x = 13.5 m/s

initial vertical momentum = final vertical momentum

0 + 0 = m * 9 * sin(60) + m * v_y

v_y = -7.79 m/s

resultant speed = sqrt(13.5^2 + 7.79^2)

speed of ball 2 after collision = 15.586 m/s

angle = 360 - tan^-1(7.79 / 13.5)

angle = 330.01 degree counterclockwise from +x axis

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