Pumpkins in Flight
1. Punkin' Droppin'
At Old Dominion University in Norfolk, Virginia, physics students have their own flying pumpkin contest. Each year they see who can drop pumpkins on a target from 10 stories up in a tall building while listening to music by the group “Smashing Pumpkins.”
By timing the flight of the falling pumpkins, the students can test scientific discoveries made by Galileo nearly 400 years ago. Galileo used clever experiments to discover that gravity exerts force on any free falling object so that d, the distance fallen, will be related to time t by the function:
d = 16t^2 (time in seconds and distance in feet)
This formula ignores the resisting effects of the air as the pumpkin falls, but it will model the flight for most compact and heavy objects quite well.
Make a table below to show estimates for the pumpkin’s distance fallen and height above the ground in feet at various times between 0 and 3 seconds at 1/2 second intervals.
Imagine pointing a punkin' chunkin' cannon straight upward from the barrel of a compressed-air cannon at a point 20 feet above the ground, at a speed of 90 feet per second (about 60 miles per hour).
3a. The height would ___________________________________
3b. h = ________________________________________
3c. For a velocity of 120 ft/sec, h = _________________________________________
3d. For a height of 15 feet above the ground, h = __________________________
4a. If height = 20 feet and the initial upward velocity is 90 ft/sec, h = ________________________
4b. If height = 15 feet and the initial upward velocity is 120 ft/sec, h = _____________________