NOVA Math 271 Project: Throwing Up Tennis Balls
You will throw a ball (preferably a tennis ball or other “soft ball”) straight up in the air, releasing the ball at shoulder height. Based on data collected, you will calculate its position function, its velocity function, and its acceleration function. Based on those functions you will answer questions below. Remember, in meters, the position function for a ball in free-fall is y(t) = -4.9t2 + v0t + y0.
What you will turn in to me : You will turn into me a poster or Powerpoint or report that shows:
a. A picture or drawing of you throwing the ball.
b. This Project Paper with the answers to questions 2-10, showing all calculations.
c. A nice, clear graph showing all three functions graphed on the same coordinate axes.
Part 1: The Equations :
Step 1: You will throw a ball up in the air with an underhand motion. (Using this motion, you should release the ball at approximately shoulder height. Have a partner measure your shoulder height in meters (to the nearest hundredth of a meter) and record here:__________. This is your initial position, y0.
Step 2: You will watch the ball go up, then watch it come back down (DON’T GET HIT BY IT!). You will time the ball and record the total time from toss to the time it hits the ground. Record the time here: ____________. This is your time final, tf .
Step 3: Now, it is time to figure out your position function. Your shoulder height is y0. So, use the fact that the position at time final is 0 (i.e., y(tf ) = 0) to calculate the ball’s initial velocity, v0 . Now you know the position function completely.
Step 4: Write your position function: __________________________
Step 5: Find your velocity function:___________________________
Step 6: Find your acceleration function: _________________________
Part 2: Graphs
Graph the position function, the velocity function, and the acceleration function on the same set of coordinate axes. Attach it to this on a separate sheet of paper. (Use WINPLOT!!)
Part 3: Questions/Analysis (Show all intermediate calculations below. Do NOT simply put answers down.):
1) Use your velocity function to calculate the TIME the ball reached its maximum height. (Hint: What is the ball’s velocity at the top of the toss?)
2) Use your position function to calculate the MAX HEIGHT at that time from Question 2.
3) Use you velocity function to calculate the ball’s velocity as it hit the ground.
4) What was the ball’s speed as it hit the ground?
5) Using the graph of your functions , answer the following (explain your answer):
a) On what intervals is your velocity positive? Negative?
b) On what intervals is your acceleration positive? Negative?
c) On what interval(s) of time is the velocity decreasing? Increasing?
d) On what intervals of time is the speed decreasing? Increasing?
6) Based on your answers to the questions above, answer the following.
a) In the interval of time when the ball is going up:
What is the sign of the velocity ? ______
What is the sign of the acceleration? ________
On that interval is the speed increasing or decreasing? ___________
b) In the interval of time when the ball is coming down:
What is the sign of the velocity? __________
What is the sign of the acceleration? _______
On that interval is the speed increasing or decreasing?___________
7) Base your answers in Number 6, above, write a conjecture as to how you would determine whether a particle is speeding up or slowing down at a specific point in time.