A golfer takes two putts to get his ball into the hole once he is on the green. The first putt displaces the ball 6.90 m east, the second 7.70 m south. What displacement would have been needed to get the ball into the hole on the first putt?
V1 = (6.90m,0 deg).
V2 = (7.7m,270 deg).
X = hor. = 6.90cos(0) + 7.7cos270,
X = 6.90 + 0 = 6.90m.
Y = ver. = 6.90sin(0) + 7.7sin270,
Y = 0 + (-7.7) = -7.7m.
tanA = Y / X = -7.7 / 6.9 = -1.1159,
A = -48.1 deg,CW.
A = -48.1 + 360 = 312 deg.,CCW.
D = X / cosA = 6.90 / cos312 = 10.3m @
312 deg.
To find the displacement needed to get the ball into the hole on the first putt, we need to consider the motion of the ball. Since the first putt displaced the ball 6.90 m east and the second putt displaced it 7.70 m south, we can treat these displacements as vectors.
We can represent the 6.90 m east displacement as a vector component in the x-direction and the 7.70 m south displacement as a vector component in the y-direction.
First, let's define our coordinate system. We can choose the east direction as the positive x-axis, and the south direction as the positive y-axis.
The 6.90 m east displacement can be represented as a vector component: (6.90 m, 0 m)
The 7.70 m south displacement can be represented as a vector component: (0 m, -7.70 m)
Now, to find the displacement needed to get the ball into the hole on the first putt, we need to find the vector sum of the two displacements.
To do this, we can add the vector components together.
(6.90 m, 0 m) + (0 m, -7.70 m) = (6.90 m, -7.70 m)
So, the displacement needed to get the ball into the hole on the first putt would be (6.90 m, -7.70 m).
To find the displacement needed to get the ball into the hole on the first putt, we can use vector addition.
First, let's represent the first putt displacement as a vector in the coordinate system. The displacement to the east is 6.90 m, so we can represent it as a vector in the positive x-direction as (6.90 m, 0 m).
Next, we represent the second putt displacement as a vector in the coordinate system. The displacement to the south is 7.70 m, so we can represent it as a vector in the negative y-direction as (0 m, -7.70 m).
To get the displacement needed for the first putt, we need to add the vectors representing the displacements of the first and second putts.
Adding the vectors:
(6.90 m, 0 m) + (0 m, -7.70 m) = (6.90 m, -7.70 m)
Therefore, the displacement needed to get the ball into the hole on the first putt is 6.90 m east and 7.70 m north.