One of the holes on a golf course lies due east of the tee. A novice golfer flubs his tee shots so that the ball lands only 64 m directly northeast of the tee. He then slices the ball 30 degrees south of east so that the ball lands in a sand trap 127 m away. Frustrated, the golfer then blasts the ball out of the sand trap, and the ball lands at a point 73 m away at an angle 27 degrees north of east. At this point, the ball is on the putting green and 14.89 m due north of the hole. To his amazement, the golfer then sinks the ball with a single shot.

Question

One of the holes on a golf course lies due east of the tee. A novice golfer flubs his tee shots so that the ball lands only 64 m directly northeast of the tee. He then slices the ball 30 degrees south of east so that the ball lands in a sand trap 127 m away. Frustrated, the golfer then blasts the ball out of the sand trap, and the ball lands at a point 73 m away at an angle 27 degrees north of east. At this point, the ball is on the putting green and 14.89 m due north of the hole. To his amazement, the golfer then sinks the ball with a single shot.

1. In the space provided, choose a scale, then draw a sketch of the displacement for each shot the golfer made. Label the magnitude of each vector and the angle of each vector relative to the horizontal axis.

I am really bad at diagraming things, so can somebody list step by step how I would sketch this problem?

2. Use algebraic formulas to find x and y components of each displacement vector.

Shot 1 x component _______ y component _______
Shot 2 x component _______ y component _______
Shot 3 x component _______ y component _______
Shot 4 x component _______ y component _______

I just need to know what algebraic formulas I would use to solve this problem.

Thanks.

Vertical component= velocity*sinTheta
Horizonal component=velocity*cosTheta

You really should understand why these are so.....If you don't understand it, you are in big trouble ahead.

Answer 1

I need the answer

Answer 2

1. To sketch the displacement for each shot, follow these steps:

- Start by drawing a horizontal line to represent the tee.
- From the tee, draw a vector that is 64 m long and directed northeast. Label this vector "Shot 1".
- From the end of Shot 1, draw a vector that is 127 m long and directed 30 degrees south of east. Label this vector "Shot 2".
- From the end of Shot 2, draw a vector that is 73 m long and directed 27 degrees north of east. Label this vector "Shot 3".
- From the end of Shot 3, draw a vector that is 14.89 m long and directed due north. Label this vector "Shot 4".
- Finally, label the magnitude of each vector and the angle of each vector relative to the horizontal axis.

2. To find the x and y components of each displacement vector, use the following formulas:

Shot 1:
- Magnitude: 64 m
- Angle relative to the horizontal axis: 45 degrees (since it is directed northeast)
- x component: 64 cos(45) = 45.25 m
- y component: 64 sin(45) = 45.25 m

Shot 2:
- Magnitude: 127 m
- Angle relative to the horizontal axis: -60 degrees (30 degrees south of east)
- x component: 127 cos(-60) = 63.5 m
- y component: 127 sin(-60) = -110.11 m

Shot 3:
- Magnitude: 73 m
- Angle relative to the horizontal axis: 63 degrees (27 degrees north of east)
- x component: 73 cos(63) = 34.84 m
- y component: 73 sin(63) = 62.78 m

Shot 4:
- Magnitude: 14.89 m
- Angle relative to the horizontal axis: 90 degrees (due north)
- x component: 0 m
- y component: 14.89 m

Answer 3

To sketch the displacements, you can follow these steps:

1. Start by drawing a horizontal line to represent the x-axis.
2. From the left end of the x-axis, draw a vertical line upward to represent the y-axis.
3. Label the endpoints of the x-axis as "Tee" and "Green" for the starting and ending points of the golfer's shots.
4. Based on the given information, draw a line segment from the Tee to the point where the first shot landed, 64 m northeast of the tee. Label this segment with its magnitude (64 m) and angle relative to the horizontal axis.
5. From the endpoint of the first shot, draw another line segment at a 30-degree angle south of east to represent the second shot. Label this segment with its magnitude (127 m) and angle relative to the horizontal axis.
6. From the endpoint of the second shot, draw another line segment at a 27-degree angle north of east to represent the third shot. Label this segment with its magnitude (73 m) and angle relative to the horizontal axis.
7. Finally, draw a line segment from the endpoint of the third shot to the point on the Green that is 14.89 m due north of the hole. Label this segment with its magnitude (14.89 m) and angle relative to the horizontal axis. This represents the final location of the ball, where the golfer sinks it.

Now let's move on to finding the x and y components for each displacement vector using algebraic formulas.

For each shot:

1. Shot 1:
- Magnitude: 64 m
- Angle relative to the horizontal axis: 45 degrees (since it lands northeast)
- X component: 64 m * cos(45) (using the formula horizontal component = velocity * cos(theta))
- Y component: 64 m * sin(45) (using the formula vertical component = velocity * sin(theta))

2. Shot 2:
- Magnitude: 127 m
- Angle relative to the horizontal axis: 150 degrees (since it is 30 degrees south of east)
- X component: 127 m * cos(150)
- Y component: 127 m * sin(150)

3. Shot 3:
- Magnitude: 73 m
- Angle relative to the horizontal axis: 63 degrees (since it is 27 degrees north of east)
- X component: 73 m * cos(63)
- Y component: 73 m * sin(63)

4. Shot 4:
- Magnitude: 14.89 m
- Angle relative to the horizontal axis: 0 degrees (it is due north)
- X component: 0 m (since it is directly north, there is no horizontal displacement)
- Y component: 14.89 m (since it is due north, the entire magnitude is in the y direction)

Remember to substitute the angles in radians when using the trigonometric functions.

I hope this helps! Let me know if you have any further questions.