Serway & Jewett — Circular Motion and Other Applications of Newton's Laws: Problem 47

A golfer tees off from a location precisely at \(\phi_i = 35.0^\circ\) north latitude. He hits the ball due south, with range \(285 \text{ m}\). The ball’s initial velocity is at \(48.0^\circ\) above the horizontal. Suppose air resistance is negligible for the golf ball. (a) For how long is the ball in flight? The cup is due south of the golfer’s location, and the golfer would have a hole-in-one if the Earth were not rotating. The Earth’s rotation makes the tee move in a circle of radius \(R_E \cos \phi_i = (6.37 \times 10^6 \text{ m}) \cos 35.0^\circ\) as shown in Figure P6.47. The tee completes one revolution each day. (b) Find the eastward speed of the tee relative to the stars. The hole is also moving east, but it is \(285 \text{ m}\) farther south and thus at a slightly lower latitude \(\phi_f\). Because the hole moves in a slightly larger circle, its speed must be greater than that of the tee. (c) By how much does the hole’s speed exceed that of the tee? During the time interval the ball is in flight, it moves upward and downward as well as southward with the projectile motion you studied in Chapter 4, but it also moves eastward with the speed you found in part (b). The hole moves to the east at a faster speed, however, pulling ahead of the ball with the relative speed you found in part (c). (d) How far to the west of the hole does the ball land?