The figureFigure1 shows a collision between three balls of c

The figure(Figure1) shows a collision between three balls of clay. The three hit simultaneously and stick together. What is the speed of the resulting blob of clay? Express your answer using two significant figures. What is the direction of the resulting blob of clay? Express your answer using two significant figures.

Solution

Momentum Before = (0.040 * 4 * cos(45)) - (0.03 * 3) = 0.023

Momentum After = 0.023 = m_after * v_x

v_x = 0.023 / m_after = 0.023 / (0.04 + 0.03 + 0.02)

v_x = 0.257 m/s

Consider y direction Momentum before = 0.04 * ( -4 * sin(45)) + 0.02 * 2 = -0.0731

-0.0731 = m_after * v_y

v_y = -0.0731 / (0.04 + 0.03 + 0.02 )

v_y = -0.813

speed = sqrt (v_x² + v_y²) = sqrt (0.257² + 0.813²)

speed = 0.853 m/s

theta = tan^-1 [0.813 / 0.257]

theta = -72.44 degrees

[ in the positive x direction and negative y direction ]