Billiard ball A of mass m_A = 0.125 kg moving with speed v_A = 2.50 m/s strikes

Question

Billiard ball A of mass m_A = 0.125 kg moving with speed v_A = 2.50 m/s strikes ball B, initially at rest, of mass m_B = 0.135 kg. As a result of the collision, ball A is deflected off at an angle of 27.5 degree with a speed v_A1 = 2.25 m/s. Express your answer symbolically in terms of the variables m_A, m_B, v_A, V_A1 Solve these equations for the speed, v_B1, of ball B. Do not assume the collision Express your answer numerically with the appropriate units. Solve these equations for the angle, theta_B, of ball B. Do not assume the collision is Express your answer numerically with the appropriate units.

Explanation / Answer

c)

here

for x

0.125 * 2.5 = 0.125 * 2.25 * cos27.5 - 0.135 * vb1 * cos(theta)

vb1 * cos(theta) = 0.467 m/s

then

for y

0 = 0.125 * 2.25 * sin(27.5deg) - 0.135 * vb1 * sin(theta)

vb1 * sin(theta) = 0.961 m/s

then the magnitude is

vb1 = sqrt(0.961^2 + 0.467^2)

vb1 = 1.068 m/s

d)

then the direction is

theta = tan^-1(0.961 / 0.467)

theta = 64.08 deg

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