11. Momentum & Impulse

(III) Two billiard balls in contact with each other are struck by a third ball moving at 5.5 m/s as shown in Fig. 9–46a. If both of the first two balls move after the collision at an angle of 32° to the initial path of the third ball (Fig. 9–46b), find the velocities of all three balls after the collision. Assume all balls have the same mass, and the collision is elastic.

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In order to convert a tough split in bowling, it is necessary to strike the pin a glancing blow as shown in Fig. 9–64. Assume that the bowling ball, traveling at 14.0 m/s just before it strikes the pin, has five times the mass of a pin and that the pin goes off at 75° from the original direction of the ball. Calculate the speed

(a) of the pin and (b) of the ball just after collision, and

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The gravitational slingshot effect. Figure 9–62 shows the planet Saturn moving in the negative 𝓍 direction at its orbital speed (with respect to the Sun) of 9.6 km/s. The mass of Saturn is 5.69 x 10²⁶ kg. A spacecraft with mass 825 kg approaches Saturn. When far from Saturn, it moves in the +𝓍 direction at 10.4 km/s. The gravitational attraction of Saturn (a conservative force) acting on the spacecraft causes it to swing around the planet (orbit shown as dashed line) and head off in the opposite direction. Using momentum conservation in one dimension, estimate the final speed of the spacecraft after it is far enough away to be considered free of Saturn’s gravitational pull. Assume the spacecraft does not affect the orbit of Saturn whose mass is so much larger.

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A 5.5-kg object moving in the +𝓍 direction at 6.5 m/s collides head-on with an 8.0-kg object moving in the ―𝓍 direction at 4.0 m/s. Determine the final velocity of each object if:

(b) the collision is elastic;