SHOT OUT OF A CANNON

In 1929, John Ringling spotted Zacchini family cannonballs at Tivoli Gardens in Copenhagen. He brought the family into his circus and began sending the five members flying through the air with his high wire projectile acts. By using air pressure, the family was able to reach an initial upward velocity of up to 110 feet per second- sending the flyer over 2 Ferris wheels.

Assuming the cannon is about 6 feet tall, the equation describing the human cannonball flight would be y= -16x2 + 110x + 6. In the equation x represents time in seconds and y represents height in feet.

a) Complete the table to compare time in seconds (x) and height in feet (y).

x (Time in seconds) y (Height in feet012345678

b) Graph the relationship. Ignore the diamonds. (Label the vertex, axis of symmetry, x and y intercepts, domain and range.)

c) What is the maximum height that Mario Zacchini would reach if he were shot from this cannon based on the data? (How do you know?)

d) After how many seconds would Mario hit the ground? (Height of 0) Explain how you know.

e) Suppose a net is placed 20 feet above the ground. After how many seconds would he hit the net? (Use quadratic formula to solve.)

f) If Mario is being shot over a 100 feet tall Ferris wheel, during what time period is he above the Ferris wheel? Explain your reasoning.

g) A hanging trapeze person plans to catch Mario at the peak of his flight and swing him back to safety. However, the hanging trapeze cannot go above 100 feet high. Change the initial velocity of the function and try to determine how fast Mario needs to be shot out of the cannon so that his maximum height reached will be 100 feet. (Use graphing calculator.)

Be careful in your calculations. If you are off by more than a few feet it could be deadly.What initial velocity did you get to work?