A golfer takes two putts to sink his ball in the once he is on the green. The first putt displaces the ball 6.00 m east, and the second putt displaces it 5.40 m south.
What displacement would put the ball in the hole in one putt?
and how do I show this graphically?
Those two putts that led to the cup were at right angles. So, take the hypotenuse
sqrt[(6^2 + 5.4^2] = ?
Why do it graphically?
If you must, draw the situation (a right triangle) on graph paper.
To find the displacement needed to put the ball in the hole in one putt, we can use the concept of vector addition. The displacement is a vector quantity, which means it has both magnitude and direction. By adding the displacements of the two putts together, we can determine the resultant displacement.
In this case, the first putt displacement of 6.00 m east can be represented as a vector pointing towards the east direction with a magnitude of 6.00 m. The second putt displacement of 5.40 m south can be represented as a vector pointing towards the south direction with a magnitude of 5.40 m.
To find the resultant displacement, we can simply add these two vectors together. Since the first putt is in the east direction and the second putt is in the south direction, we can imagine creating a right-angled triangle with the two vectors as its sides.
Using the Pythagorean theorem for right triangles, the magnitude of the resultant displacement can be found:
Resultant Displacement = √[(6.00 m)² + (5.40 m)²] = √[36.00 m² + 29.16 m²] = √65.16 m² ≈ 8.08 m
The direction of the resultant displacement can be calculated using trigonometry. Since the first putt is in the east direction, and the south direction is 90 degrees clockwise from the east, we can determine the angle using the inverse tangent function:
Angle = arctan(5.40 m / 6.00 m) ≈ 43.40 degrees
Therefore, the displacement that would put the ball in the hole in one putt is approximately 8.08 m in magnitude, at an angle of 43.40 degrees south of east.
To show this graphically, you can use a coordinate system. Draw an x-y plane with the south direction as the positive y-axis and the east direction as the positive x-axis. Start from the origin (0,0) and draw a vector of length 6.00 m in the east direction. Then, from the endpoint of the first putt vector, draw another vector of length 5.40 m in the south direction. The endpoint of this second vector will represent the resultant displacement, which is the hypothetical one-putt displacement that puts the ball in the hole.
You can label the magnitudes and the directions on the graph to visually represent the solution.