A golf tee is located at precisely ; = 46.5° north latitude, as shown in the figure below. The hole that the golfer is aiming for is directly south of the tee, a distance of 370 m. The golfer hits the ball from this tee with an initial velocity that is 48.0° above the horizontal, and the horizontal component of the ball's initial velocity is directly south. The horizontal range that the golf ball travels in flight is also 370 m, but the golfer is surprised to find that the golf ball does not land in the hole. We will assume that air resistance is negligible for the golf ball. The questions below analyze how the Earth's rotation affects the golf ball's apparent trajectory. North Pole Radius of circular path of tee RECOS ; RE Tee Golf ball trajectory -Hole Equator (a) For what length of time is the ball in flight (in s)? S (b) From the point of view of the golf tee, the ball's horizontal velocity is directed south. However, the golf tee, and therefore the golf ball, are moving east due to the rotation of the Earth. The tee moves in a circle of radius R cos(;) = (6.371008 × 106 m)cos(46.5°), as shown in the figure, and completes one revolution per day. What is the eastward speed of the tee (in m/s)? (Assume there are 23.93447 hours in one day. Round your answer to at least three decimal places.) m/s (c) The hole is also moving east, but it is 370 m farther south and thus at a slightly lower latitude Op. By how much does the eastward speed of the hole exceed that of the tee? (Give your answer in m/s.) m/s (d) Because the tee has an eastward speed, the ball therefore has an eastward velocity component equal to the speed found in part (b), in addition to its vertical and southward velocity components. But because the hole moves to the east at a faster speed, it pulls ahead of the ball with the relative speed you found in part (c). From the point of view of the golf tee, the ball appears to drift to the west. How far (in cm) to the west of the hole does the ball land? cm
A golf tee is located at precisely ; = 46.5° north latitude, as shown in the figure below. The hole that the golfer is aiming for is directly south of the tee, a distance of 370 m. The golfer hits the ball from this tee with an initial velocity that is 48.0° above the horizontal, and the horizontal component of the ball's initial velocity is directly south. The horizontal range that the golf ball travels in flight is also 370 m, but the golfer is surprised to find that the golf ball does not land in the hole. We will assume that air resistance is negligible for the golf ball. The questions below analyze how the Earth's rotation affects the golf ball's apparent trajectory. North Pole Radius of circular path of tee RECOS ; RE Tee Golf ball trajectory -Hole Equator (a) For what length of time is the ball in flight (in s)? S (b) From the point of view of the golf tee, the ball's horizontal velocity is directed south. However, the golf tee, and therefore the golf ball, are moving east due to the rotation of the Earth. The tee moves in a circle of radius R cos(;) = (6.371008 × 106 m)cos(46.5°), as shown in the figure, and completes one revolution per day. What is the eastward speed of the tee (in m/s)? (Assume there are 23.93447 hours in one day. Round your answer to at least three decimal places.) m/s (c) The hole is also moving east, but it is 370 m farther south and thus at a slightly lower latitude Op. By how much does the eastward speed of the hole exceed that of the tee? (Give your answer in m/s.) m/s (d) Because the tee has an eastward speed, the ball therefore has an eastward velocity component equal to the speed found in part (b), in addition to its vertical and southward velocity components. But because the hole moves to the east at a faster speed, it pulls ahead of the ball with the relative speed you found in part (c). From the point of view of the golf tee, the ball appears to drift to the west. How far (in cm) to the west of the hole does the ball land? cm
Principles of Physics: A Calculus-Based Text
5th Edition
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Author:Raymond A. Serway, John W. Jewett
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Chapter3: Motion In Two Dimensions
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Transcribed Image Text:A golf tee is located at precisely ; = 46.5° north latitude, as shown in the figure below. The hole that the golfer is aiming for is directly south of the tee, a distance of 370 m. The golfer hits the ball from this tee with an initial velocity that is 48.0° above the horizontal, and the horizontal
component of the ball's initial velocity is directly south. The horizontal range that the golf ball travels in flight is also 370 m, but the golfer is surprised to find that the golf ball does not land in the hole. We will assume that air resistance is negligible for the golf ball. The questions below
analyze how the Earth's rotation affects the golf ball's apparent trajectory.
North
Pole
Radius of circular
path of tee
RECOS ;
RE
Tee Golf ball
trajectory
-Hole
Equator
(a) For what length of time is the ball in flight (in s)?
S
(b) From the point of view of the golf tee, the ball's horizontal velocity is directed south. However, the golf tee, and therefore the golf ball, are moving east due to the rotation of the Earth. The tee moves in a circle of radius R cos(;) = (6.371008 × 106 m)cos(46.5°), as shown in the
figure, and completes one revolution per day. What is the eastward speed of the tee (in m/s)? (Assume there are 23.93447 hours in one day. Round your answer to at least three decimal places.)
m/s
(c) The hole is also moving east, but it is 370 m farther south and thus at a slightly lower latitude Op. By how much does the eastward speed of the hole exceed that of the tee? (Give your answer in m/s.)
m/s
(d) Because the tee has an eastward speed, the ball therefore has an eastward velocity component equal to the speed found in part (b), in addition to its vertical and southward velocity components. But because the hole moves to the east at a faster speed, it pulls ahead of the ball with
the relative speed you found in part (c). From the point of view of the golf tee, the ball appears to drift to the west. How far (in cm) to the west of the hole does the ball land?
cm
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