Vector of golfer problem

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In summary, a novice golfer takes three strokes to sink the ball, with successive displacements of 3.90 m north, 2.10 m northeast, and 1.00 m at 30.0° west of south. An expert golfer could make the hole in one single displacement, which could be found by summing the x and y components of each vector and connecting the origin of the first vector with the arrow of the last. The angle of this single displacement can also be determined.
  • #1
balling12
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Homework Statement


A novice golfer on the green takes three strokes to sink the ball. The successive displacements are 3.90 m to the north, 2.10 m northeast, and 1.00 m at 30.0° west of south. Starting at the same initial point, an expert golfer could make the hole in what single displacement? At what angle?



Homework Equations





The Attempt at a Solution


I attempted to draw the diagram of the situation and that is as far as i have got.
 
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  • #2
balling12 said:

Homework Statement


A novice golfer on the green takes three strokes to sink the ball. The successive displacements are 3.90 m to the north, 2.10 m northeast, and 1.00 m at 30.0° west of south. Starting at the same initial point, an expert golfer could make the hole in what single displacement? At what angle?



Homework Equations





The Attempt at a Solution


I attempted to draw the diagram of the situation and that is as far as i have got.
Drawing a diagram is an excellent start. Now connect the origin of the first vector with the arrow of the last, and that's the resultant displacement. You can solve for it by several ways; try summing the x and y components of each vector to get the resultant x and y components,(are you familiar with this??). Please show your work so we may assist.
 
  • #3


I would approach this problem by first analyzing the given information and identifying the relevant equations and principles that can be applied. From the given information, it is clear that the novice golfer takes three strokes to sink the ball and the successive displacements are given. This suggests that the problem can be solved using vector addition.

The relevant equations to use in this case would be the Pythagorean theorem and the law of cosines. The Pythagorean theorem can be used to find the magnitude of the final displacement, while the law of cosines can be used to find the angle of the final displacement.

Using the Pythagorean theorem, we can find the magnitude of the novice golfer's final displacement as:

√(3.90^2 + 2.10^2 + 1.00^2) = 4.56 m

Next, we can use the law of cosines to find the angle of the final displacement:

cosθ = (b^2 + c^2 - a^2) / 2bc

Where a = 4.56 m, b = 2.10 m, and c = 1.00 m.

Substituting these values into the equation, we get:

cosθ = (4.56^2 + 1.00^2 - 2.10^2) / (2 * 4.56 * 1.00)

Solving for θ, we get:

θ = 39.3°

Therefore, an expert golfer can make the hole in a single displacement of 4.56 m at an angle of 39.3° west of south.

In conclusion, by using the principles of vector addition and relevant equations, we can determine the final displacement and angle that an expert golfer would need to make the hole in a single stroke. This problem highlights the importance of understanding and applying mathematical concepts in real-world scenarios.
 

1. What is the "Vector of golfer problem"?

The "Vector of golfer problem" is a mathematical optimization problem that seeks to find the optimal path for a golfer to take on a golf course in order to minimize the total distance traveled between holes.

2. What are the key variables in the "Vector of golfer problem"?

The key variables in the "Vector of golfer problem" are the location of each hole on the golf course, the starting point of the golfer, and the path that the golfer takes between holes.

3. How is the "Vector of golfer problem" solved?

The "Vector of golfer problem" is typically solved using mathematical optimization techniques, such as dynamic programming or genetic algorithms, to find the shortest path between holes that minimizes the total distance traveled.

4. What are the real-world applications of the "Vector of golfer problem"?

The "Vector of golfer problem" has real-world applications in sports, logistics, and transportation industries. It can be used to optimize routes for golfers, delivery drivers, and public transportation systems.

5. What are some challenges in solving the "Vector of golfer problem"?

Some challenges in solving the "Vector of golfer problem" include the large number of variables and possible paths to consider, as well as the need for accurate data on the golf course layout and golfer behavior. Additionally, the problem becomes increasingly complex with the addition of obstacles, such as trees or water hazards, on the course.

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