45. ssm Consult Multiple-Concept Example 9 in preparation for this problem. A golfer, putting on a green, requires three strokes to "hole the ball." During the first putt, the ball rolls 5.0 m due east. For the second putt, the ball travels 2.1 m at an angle of 20.0° north of east. The third putt is 0.50 m due north. What displacement (magnitude and direction relative to due east) would have been needed to "hole the ball" on the very first putt?
45. ssm Consult Multiple-Concept Example 9 in preparation for this problem. A golfer, putting on a green, requires three strokes to "hole the ball." During the first putt, the ball rolls 5.0 m due east. For the second putt, the ball travels 2.1 m at an angle of 20.0° north of east. The third putt is 0.50 m due north. What displacement (magnitude and direction relative to due east) would have been needed to "hole the ball" on the very first putt?
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ISBN:9781305952300
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Chapter1: Units, Trigonometry. And Vectors
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Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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![### Problem 45
#### Physics - Displacement and Vector Addition
Consult Multiple-Concept Example 9 in preparation for this problem.
A golfer, putting on a green, requires three strokes to "hole the ball." During the first putt, the ball rolls 5.0 meters due east. For the second putt, the ball travels 2.1 meters at an angle of 20.0° north of east. The third putt is 0.50 meters due north.
**Question:** What displacement (magnitude and direction relative to due east) would have been needed to "hole the ball" on the very first putt?
**Steps for Solving:**
1. **First Putt:**
- Distance: 5.0 meters
- Direction: Due east
2. **Second Putt:**
- Distance: 2.1 meters
- Direction: 20.0° north of east
3. **Third Putt:**
- Distance: 0.50 meters
- Direction: Due north
**Solution Approach:**
1. Break down the second putt into its components using trigonometry:
- \( x_{2} = 2.1 \cos(20°) \)
- \( y_{2} = 2.1 \sin(20°) \)
2. Sum up the x and y components for the total displacement:
- \( x_{total} = 5.0 + x_{2} \)
- \( y_{total} = y_{2} + 0.50 \)
3. Calculate the resultant displacement using Pythagorean theorem:
- \( d = \sqrt{x_{total}^2 + y_{total}^2} \)
4. Determine the direction (angle) relative to due east:
- \( \theta = \tan^{-1}(y_{total} / x_{total}) \)
By following these steps, it is possible to find the displacement needed for the ball to reach the hole in just one stroke.
Note: There are no graphs or diagrams provided in the text. However, if you're learning about vector addition, consider drawing a diagram with the vectors to visualize the problem better.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb2c8c9d8-cb7d-4bb3-b241-ba372e4ba26e%2F4699ade9-a8ab-4f1c-bb40-4d3e21da58c6%2Fsy8vgg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem 45
#### Physics - Displacement and Vector Addition
Consult Multiple-Concept Example 9 in preparation for this problem.
A golfer, putting on a green, requires three strokes to "hole the ball." During the first putt, the ball rolls 5.0 meters due east. For the second putt, the ball travels 2.1 meters at an angle of 20.0° north of east. The third putt is 0.50 meters due north.
**Question:** What displacement (magnitude and direction relative to due east) would have been needed to "hole the ball" on the very first putt?
**Steps for Solving:**
1. **First Putt:**
- Distance: 5.0 meters
- Direction: Due east
2. **Second Putt:**
- Distance: 2.1 meters
- Direction: 20.0° north of east
3. **Third Putt:**
- Distance: 0.50 meters
- Direction: Due north
**Solution Approach:**
1. Break down the second putt into its components using trigonometry:
- \( x_{2} = 2.1 \cos(20°) \)
- \( y_{2} = 2.1 \sin(20°) \)
2. Sum up the x and y components for the total displacement:
- \( x_{total} = 5.0 + x_{2} \)
- \( y_{total} = y_{2} + 0.50 \)
3. Calculate the resultant displacement using Pythagorean theorem:
- \( d = \sqrt{x_{total}^2 + y_{total}^2} \)
4. Determine the direction (angle) relative to due east:
- \( \theta = \tan^{-1}(y_{total} / x_{total}) \)
By following these steps, it is possible to find the displacement needed for the ball to reach the hole in just one stroke.
Note: There are no graphs or diagrams provided in the text. However, if you're learning about vector addition, consider drawing a diagram with the vectors to visualize the problem better.
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