Parametric Graphing : The Perfect Foul Shot

Questions

1. Would the ball have hit a 15-foot ceiling on this shot?

2. When was the ball 10 feet horizontally from the shooter?
Try changing the velocity but not the angle: Press [HOME] 30 STO [ALPHA][V] [ENTER] (The angle will remain 70 degrees if you don't change it.) Press [PLOT] [PLOT] Hmmm... maybe it banked in, but you're supposed to ignore that possibility.

3. What is the maximum height the ball traveled that time?

4. When was the ball horizontally 14.5 feet from the shooter? Yep, that's a long time for the ball to be in the air. Things are not quite right yet. But now everything is set to explore and find the velocity and angle for The Perfect Shot. (Decimal values for angles and velocity are fine.)

5. Keeping the angle at 70 degrees, change the velocity until the ball goes in. Trace on the path and make sure the cursor goes through the target area. How much time until the ball travels downward through the plane of the hoop? Keep a record of the velocities and the results. Even in problem #1, the time was longer than for an average good shot. Vary the velocity and the angle to get something more reasonable.

6. Find an appropriate velocity and angle for a shot which takes about 1 second to enter the target. How high did it go? Keep a record of angle, velocity and the time.

7. Find a velocity to go with a 72 degrees angle. Trace to see more time even if it appears that the ball stops in midair. Would it hit a 20-foot ceiling?

8. With an initial velocity of 27 ft / sec., find an appropriate angle.

9. Is a 2.5-second shot appropriate? Justify your answer.

Answers:

1.No.

2.Approximately 1.27 seconds.

3. Approximately 18.42 feet.

4. Approximately 1.41 seconds.

5. Vel. (ft / s) Time (sec.) Basket?
29 1.54 no
28 1.47 yes
27 1.41 no
27.5 1.44 no
27.8 1.46 close
27.9 1.47 close
28.1 1.48 yes
28.2 1.49 yes

6.Time (sec.) Vel. (ft / s) Angle (degrees)
1.00 24.5 55
1.13 25 60
1.28 26 65

12.29 feet high at V= 24.5 and A = 55

7. 29 feet per second. No, it would not hit a 20-foot ceiling.

8. 68 degrees.

9. A shot with V = 39 and A = 81 degrees would take about 2.3 seconds. Its arc would reach 29.18 feet high, too high for most gyms and too inaccurate for most shooters.