Concept explainers
A golfer tees off from a location precisely at ϕi = 35.0° north latitude. He hits the ball due south, with range 285 m. The ball’s initial velocity is at 48.0° 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 RE cos ϕi = (6.37 × 106 m) cos 35.0° 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 cast, but it is 285 m farther south and thus at a slightly lower latitude ϕf. Because the hole moves in a slightly larger circle, its speed must he 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?
Figure P6.47
(a)
The time of flight of the ball.
Answer to Problem 6.67CP
The time for which the ball be in flight is
Explanation of Solution
The range of the motion after hitting the ball is
The range of the parabolic motion
Here,
Write the expression for the equation for parabolic motion
As initial and final distance is equal,
Rearrange the above expression for
Substitute
Rearrange the above expression for
Substitute
Conclusion:
Substitute
Therefore, the time for which the ball be in flight is
(b)
The relative eastward speed of the tee with respect to the stars.
Answer to Problem 6.67CP
The relative eastward speed of the tee with respect to the stars is
Explanation of Solution
Write the formula to calculate the eastward speed of the tee relative to the stars
Here,
Conclusion:
Substitute
Therefore, the relative eastward speed of the tee with respect to the stars is
(c)
The value by which the hole's speed exceed that of the tee.
Answer to Problem 6.67CP
The value by which the hole's speed exceed that of the tee is
Explanation of Solution
Write the formula to calculate the length of the arc
Rearrange the above expression for
Substitute
Write the formula to calculate the speed of the hole
Here,
Substitute
Calculate the difference between the speed of tee and the speed of hole.
Here,
Conclusion:
Substitute
Therefore, the value by which the hole's speed exceed that of the tee is
(d)
The distance to the west of the hole from the position where the ball lands.
Answer to Problem 6.67CP
The distance to the west of the hole from the position where the ball land is
Explanation of Solution
Write the expression for the distance to west of the hole
Here,
Conclusion:
Substitute
Therefore, the distance to the west of the hole from the position where the ball land is
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Chapter 6 Solutions
Physics for Scientists and Engineers, Volume 1
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