In this virtual laboratory you will investigate projectile motion with and without air resistance.  You will find the maximum range of a football with given initial velocity and the launch angles required for it to hit a target.

Procedure:

Open the Projectile Motion interactive animation.
 Position the canon 20 m to the left of the target, as shown below.  Make sure the cross on the canon is at the same height as the target.  The ruler should lie on the horizontal axis of the coordinate system show. Choose the football projectile and give it an initial speed of between 14 and 18 m/s.

(a)  Given the initial speed there are two launch angles for the football to hit the center of the target.
What is the smaller of these launch angles (within ~±1o)?

(b)  Given an initial speed there are two launch angles for the football to hit the center of the target.
What is the larger of these launch angles (within ~±1o)?

(c)  Given the initial speed, find the maximum range of the projectile along the horizontal rulerMeasure this distance with the ruler, do not use the number displayed by the simulation.  The simulation displays the distance traveled by the ball before it hits the ground.

(d)  Now set initial speed of the projectile at 20 m/s.  Find the maximum range of the projectile along the horizontal ruler.  For this maximum range note the launch angle and the hang time of the football and estimate the maximum height of the football above the ground during its flight.
Do this twice, once neglecting air resistance and once not neglecting air resistance  For the second case choose the drag coefficient to be 0.5.  Fill in the table below.  Compare your results with and without air rsistance.

 Projectile speed: 20 m/s Maximum range Launch angle (deg) Maximum height (m) Hang time (s) no air resistance drag coefficient 0.5

To earn extra credit go to Blackboard, Assignments, and complete the extra credit assignment 3.