Answer to Question #221059 in Physics for yang

Question

1. A 6500 g bowling ball moving at 10.00 m/s collides with a 850 g bowling pin, which is scattered at an angle to the initial direction of the bowling ball and with a speed of 15.0 m/s. a. Calculate the final velocity (magnitude and direction) of the bowling ball. b. Is the collision elastic?
2. A family is skating. The father (85 kg) skates at 6.2 m/s and collides and sticks to the mother (55 kg), who was initially moving at 3.5 m/s and at 45° with respect to the father’s velocity. The pair then collides with their daughter (25 kg), who was stationary, and the three slides off together. What is their final velocity?

Answer 1

1)

$$\theta=\arctan{\frac{(0.85)(15)\sin{15}}{(6.5)(10)-(0.85)(15)\cos{15}}}=3.58\degree$$

$$v=\frac{0.85\sin{15}}{6.5\sin{3.58}}15=8.13\frac{m}{s}$$

2)

$$v_x=\frac{85(6.2)+55(3.5)\cos{45}}{85+55+25}=4.0\frac{m}{s}\\ v_y=\frac{55(3.5)\sin{45}}{85+55+25}=0.8\frac{m}{s}\\v=\sqrt{4^2+0.8^2}=4.1\frac{m}{s}\\\theta=\arctan{\frac{0.8}{4}}=11\degree$$