Perform the following experiments and related calculations. Check your results against those displayed by the applet.

1. Set the ball to some initial position and then drag it to a final position. Use the x and y coordinates of the ball's initial and final positions to calculate the x and y components of the ball's displacement vector .
2. Using the data from the first exercise, calculate the magnitude d of the ball's displacement and the angle q between the displacement vector and the positive x-direction, taken in the positive sense (counter-clockwise starting from the x-axis).
3. Compare the green displacement vector to the blue path along which the ball has traveled. Which has the greater length? Compare the magnitude d of the displacement calculated in the previous exercise to the distance s traveled displayed by the applet.
4. Set the ball's initial position to (10,-10) m. It will make it easier if you display the grid when you do this. Then make the ball undergo a displacement equal to 30 m in magnitude and in a direction that forms an angle of 150⁰ with the positive x-axis, measured in the positive sense from the x-axis. It may be difficult to produce these values exactly. It will be good enough if you get close. From these data calculate the x and y coordinates of the ball's final position.
5. Set the ball's initial position to (20,-10) m. Then drag the ball in a straight line to (20,-20) m, again in a straight line to (-15,-20) m, and again in a straight line to (-15,15) m. It does not matter if you cannot achieve these exact values. To ensure that the ball moves along a straight line, hold down the Shift key while you are dragging the ball.

   Calculate the total displacement vector, both in Cartesian and in polar coordinates (magnitude and direction).

   Also calculate the distance s traveled and compare it to the magnitude d of the displacement.