Passage VII

Students studies the trajectories of a baseball launched under a variety of conditions.

Study 1

On a flat plain during a windless day, students launched a baseball using the launched showing in Figure 1.

A camera mounted on the launcher always pointed in the direction of the ball’s launch. A radar transceiver (transmitter-receiver) was also mounted on the launcher.

As the ball moved along its path, Angle θ, which is defined in Figure 1, continuously varied. The variation in θ was monitored by the camera, which recorded the ball’s image in its viewfinder every 0.5 sec after launch until the ball landed. For each recorded image, θ was found (see Figure 2).

In addition, every 0.5 sec after launch, the transceiver emitted a radar pulse, part of which was reflected back to the transceiver by the ball. The round-trip travel time of each pulse was recorded and then used to determine the distance, D, between the transceiver and the ball (see Figure 3).

Using D and θ, the students found the ball's height, H, and distance, R, at the end of each 0.5 sec interval. H was plotted versus R, and a smooth curve was fitted to the data points.

This procedure was followed for launches of the ball at speeds of 80 mph, 90 mph, 100 mph, 110 mph, and 120 mph. For each launch speed, the ball was launched at θ = 35°. The curves representing the 5 launch speeds were connected by lines drawn through the data points representing H and R for time = 2 sec, 3 sec, 4 sec, and 5 sec after launch (see Figure 4).

Study 2

Using a mathematical model, the students calculated H and R at 0.5 sec intervals for the same ball launched under the same conditions, as in Study 1, except that they assigned that air was absent. The results are plotted in Figure 5.