Skee Ball amusement. The popular arcade sport of Skee Ball involves bowling a wooden ball 3 in. (7.6 cm) in diameter down an alley 9 ft long, where the ball is then launched off a short ramp as shown in Figure P9.68. Highest points are awarded to those who can launch the ball such that it lands in the topmost cylindrical hole; landing in lower and larger holes is worth fewer points. The launch ramp is 8.5 cm high and slopes at an angle ? = 40?. From the top of the launch ramp, the location of the score cups for the 30-point hole and 50-point hole are (x₃₀, y₃₀) = (25 cm, 6.0 cm) and (x₅₀, y₅₀) = (42 cm, 12 cm), respectively, as shown in Figure P9.68.?

(a) If the ball rolls without slipping, what initial horizontal velocity must the ball have to make it into the 30-point hole??

(b) An expert makes a 50-point score with one ball. What were the initial linear and angular velocities of the ball??

(c) Is it likely that the ball actually does not slip while it rolls?

Figure P9.68

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