Question

A golfer takes three putts to get the ball into the hole. The first putt displaces the ball 3.34 m north, the second 1.60 m southeast, and the third 0.783 m southwest. What are (a) the magnitude and (b) the angle between the direction of the displacement needed to get the ball into the hole in just one putt and the direction due east

Answer 1

We want to find the magnitude and direction of the ball's displacement. We will see that the magnitude is 1.76m and the direction is 70.74°

What is displacement?

We define displacement as the difference between the final position and the initial position.

To define a position we first need to define a coordinate system, we will use east as the positive x-axis and north as the positive y-axis.

The ball starts at the point (0m, 0m).

First, it is displaced 3.34m to the north, so the new position is (0m, 3.34m).

Then 1.60m southeast, assuming that southeast means exactly 45° between east and south (positive x-axis and negative y-axis)

This implies that the ball moves:

• 1.60m*cos(45°) = 1.13m east
• -1.60m*sin(45°) = -1.13m north.

So the new position is:

(0m + 1.13m, 3.34m - 1.13m) = (1.13m, 2.21m)

Finally, there is a displacement of 0.783m southwest, where southwest would be an angle of 225° measured counterclockwise from the positive x-axis, so the components of motion are:

0.783m*cos(225°) = -0,55m

0.783m*sin(225°) = -0.55m

So the final position of the ball is:

(1.13m - 0.55m , 2.21m -0.55m) = (0.58m, 1.66m)

So now we have the final position, because the initial position is (0m, 0m) the magnitude of the displacement will just be the magnitude of the final position, which is:

M = √( (0.58m)^2 + (1.66m)^2 ) = 1.76m

And the direction measured from the positive x-axis (east) is given by the Arctangent of the quotient between the y-component and the x-component, so the angle is:

A = Atg(1.66m/0.58m) = 70.74°

If you want to learn more about displacement, you can read:

https://brainly.com/question/4931057