Halliday, Resnick & Walker — Oscillations: Problem Problem_106

SHM shooting gallery. Figure 15.42 shows your view of an arcade shooting gallery in which a small wooden duck oscillates along a track left and right in SHM with period \( T = 4.00 \text{ s} \) and amplitude \( x_m = 1.20 \text{ m} \). Two air rifles are fixed in place at the front of the gallery at distance \( d = 3.00 \text{ m} \) from the duck’s line of motion. Rifle A is aligned with \( x = 0 \) at the center of the motion and rifle B is aligned with \( +x_m \) at the right side of the motion. Both rifles shoot pellets at speed \( v = 9.00 \text{ m/s} \). You will win the grand prize (a giant stuffed duck, of course) if you can hit the duck with pellets from both rifles. At what value of \( +x \) (on the right side) should the duck be when you fire (a) rifle A and (b) rifle B?