A golfer takes two putts to sink his ball in the
hole once he is on the green. The first putt
displaces the ball 8.70 m east, and the second
putt displaces it 6.04 m south.
What displacement would put the ball in
the hole in one putt?
Answer in units of m
and..........
What is the direction (measured from due
east, with counterclockwise positive) of the
displacement?
Answer in units of ◦
X = 8.70 m.
Y = -6.04 m.
a. D^2 = X^2 + Y^2 = 8.7^2 + (-6.04)^2 =
112.2
D = 10.6 m.
b. Tan A = Y/X = -6.04/8.7 = -0.69425
A = -34.8o CW.
A = 360 - 34.8 = 325.2o CCW.
To find the displacement that would put the ball in the hole in one putt, we can use the concept of vector addition.
1. Draw a coordinate system with the origin at the starting point of the golfer.
2. Draw the first putt's displacement vector, which is 8.70 m east. This vector points to the right.
3. Draw the second putt's displacement vector, which is 6.04 m south. This vector points downward.
4. To find the displacement that would put the ball in the hole in one putt, we need to add these two displacement vectors together.
5. Draw arrows representing each vector and place them head-to-tail, starting from the origin.
6. The displacement vector connecting the starting point to the end point of the last displacement vector is the resultant displacement.
7. Measure the magnitude of the displacement vector using a ruler or measuring tool. This will give you the distance.
8. Measure the direction of the displacement vector using a protractor or angle measuring tool, starting from due east (along the positive x-axis) in a counterclockwise direction.
Performing the vector addition:
Draw an 8.70 m vector pointing east and a 6.04 m vector pointing south. The resultant vector connecting the tail of the first vector to the head of the second vector will be the displacement vector that would put the ball in the hole in one putt.
To find the magnitude (distance) and direction of this resultant displacement vector, use the Pythagorean theorem and trigonometric functions:
Magnitude:
Magnitude = √((8.70 m)^2 + (6.04 m)^2)
Direction:
Direction = arctan(6.04 m / 8.70 m)
Perform the calculations to find the final answers.