ShowMe - Projectile Motion: One Ball No Air

The applet shows a ball performing projectile motion without air resistance

Instructions

This page is designed to get you started using the applet. The applet should be open. The step-by-step instructions on this page are to be done in the applet. You may need to toggle back and forth between instructions and applet if your screen space is limited.

Contents

Setting the Ball's Initial Position and Velocity

Observing the Ball's Motion

Stepping Through the Motion

Setting a Target and Measuring Point Coordinates

Setting the Ball's Initial Position and Velocity

  1. Initial Position

    Click the Reset button .

    Click on the ball and drag it to the initial position (x,y) = (20.0, 10.0) m, as shown in Figure 1 below. You may find this easier to do if you display the grid by pressing the Grid toggle button . (The grid is not shown in Figure 1.)

    It also helps to adjust one coordinate at a time. Drag the ball to x = 20.0 m without worrying about the y-coordinate. Then, hold down the Shift key while dragging the ball. Now the ball will move only vertically and it will be much easier to adjust its initial y-coordinate to 10.0 m. The x-coordinate will remain unchanged while the Shift key is held down.

    Figure 1

    Notice the shadow balls on the x and y axes. They move with the ball and are projections of the ball onto the two axes. Their positions represent the ball's x and y coordinates.

    The ball's x and y position coordinates are displayed in the top right corner of the applet. These will be updated throughout the motion, along with the value t of the time elapsed. Time elapsed is measured from the beginning of the motion. Thus, at the beginning of the motion, t = 0.

  2. Initial Velocity

    The magenta arrow represents the ball's initial velocity. (During the motion it represents the ball's velocity at a given instant.) Adjust the initial velocity to a magnitude of 20 m/s and to a direction that forms an angle q with the positive x-axis equal to 60o. Do this by typing these values in the first column of the velocity data panel, shown at the bottom of Figure 1, and then press the ENTER key on the keyboard.

    Notice how the display of the x and y components of the ball's velocity is automatically adjusted to vx = 10.0 m/s and vy = 17.3 m/s. You can enter values in any of the four velocity data fields. When you press ENTER, the values in the four fields are adjusted automatically so that they are consistent. The last value entered and its partner in the same column are not adjusted.

    You can adjust the initial velocity also by dragging the tip of the velocity vector. The four velocity data fields will be adjusted accordingly.

Observing the Ball's Motion

  1. Press the Play button to start the motion. Display the ball's path by pressing the Trace toggle button .

    2. When the ball has disappeared from the applet window, press the Replay button . Press the Components toggle button to display the horizontal and vertical components of the velocity vector. Then press Play once more and pause the motion on the way up by clicking the Pause button . (Once the Play button is pressed, it changes into the Paus button, and vice versa.) You should see a display similar to that in Figure 2 below.

    Figure 2

  2. Click Replay once more. This time, step through the motion again by clicking the Step button repeatedly. Observe that the horizontal component of the velocity vector remains constant and, correspondingly, that the value of vx in the data panel stays constant at 10.0 m/s. The vertical component of the velocity is continually decreasing in magnitude on the way up, changes direction at the top, and then is continually increasing in magnitude on the way down. Correspondingly, the values of vy in the data panel are continually decreasing. (Even when they are negative they are decreasing. E.g., -10 is less than -5.)

  3. Click Replay once more and then Play. Watch the continuous motion again. Observe how the shadow ball on the x-axis moves to the right with constant velocity. Observe how the shadow ball on the y-axis performs an up-and-down motion like a ball thrown straight up.

  4. Click Replay once more. This time, change the x-component of the ball's velocity to 20 m/s without changing the y-component. Then press Play. Observe that the ball is now moving more quickly in the horizontal direction, but that its vertical motion is unaffected.

    E.g., at t = 0.87 s, the vertical position of the ball is y = 21.3 m and the y-component of velocity is 8.8 m/s in both cases, as you can check by comparing Figure 2 above and Figure 3 below. Also, comparing the two trajectories shows that the ball reaches exactly the same height in both situations.

    Figure 3

  5. As a final element in the motion, you can observe the ball's acceleration by pressing the Acceleration toggle button . The acceleration vector is shown in green.

    Replay the motion along both of the previous trajectories by setting the initial velocity component in the x-direction equal to 10.0 m/s or 20.0 m/s, without changing the initial y-component. Display the components of the velocity vector. Observe the acceleration vector, and observe the behaviour of the y component of the velocity vector during the motion. In particular, observe the acceleration vector at the moment the ball reaches the top of its trajectory.

    In this simulation where there is no air resistance, the ball's acceleration is equal to the acceleration due to gravity. You can vary the magnitude g of the acceleration due to gravity, and therefore the magnitude of the ball's acceleration, between 0 and 20 m/s by means of the g-slider .

    Click Replay and set g to 5 m/s2. Then play the motion again, with either one of the previous two initial velocities. You should observe higher trajectories this time.

Stepping Through the Motion

Click Replay and set vx to 20 m/s, but don't change the y-component of the initial velocity. Step through the motion by clicking the Step button repeatedly until you reach the same elapsed time as in Figure 3, namely, t = 0.87 s. You can do that by adjusting the Step slider .

The size of the time step used by the Step can be adjusted between 0.01 s and 1.00 s by moving the slider tab. Fine adjustments by 0.01 s can be made by clicking in the "groove" of the slider, either to the left or to the right of the tab.

First adjust the slider to a step size of 0.2 s, and take four steps until you are at t = 0.80 s. Then adjust the slider to a step size of 0.01 s, and take seven more steps until you are at t = 0.87 s. Compare the position and velocity values displayed by your applet to those shown in Figure 3 above.

Fine-tuned stepping through a motion is useful in determining the time required for the ball to reach a certain position, e.g., its maximum height, the time required to drop back down to the x-axis, or the time required to reach a target. (About targets, see the next section.)

Setting a Target and Measuring Point Coordinates

Select the Target button . Then click anywhere in the applet window. A bull's eye target will be placed at the point clicked. The (x,y)-coordinates of the target's location will be displayed as long as the mouse button is depressed. Dragging with the mouse will let you drag the target to a desired location. Click on the target a second time, and the target will removed, but only if the Target button is still selected.

The Draw-Point button functions like the target button. Select it, and click anywhere in the applet window. A dot will be placed at the point clicked, and the (x,y)-coordinates of the dot will be displayed. This way you can measure the coordinates of a point. The dot can be dragged to a new location as long as the mouse button is depressed. Click on the dot a second time, and the dot will be removed, but only if the Draw-Point button is still selected.

Exercise. Set a target and find an initial velocity so that the ball will hit the target.