Reference no: EM13887596
Part A -
You toss a pumpkin up into the air and off the building. You are careful to throw exactly vertically, a few feet from the edge of the building so that the pumpkin will not hit the building on the way back down. The height of your hand from the ground, at the time you release the pumpkin, i.e. t=0, is 48 feet.
The initial vertical velocity of the pumpkin is 56 fps. And its height above the ground at any time, t, is given by:
h(t) = -16.1t2 + (initial speed)*t + initial height (ft)
h(t) = -16.1t2 + 56*t + 48 (ft)
a. At what times is the pumpkin at exactly 48 feet above the ground?
b. What is the time required for the pumpkin to hit the ground?
c. What is the maximum height that the pumpkin reaches?
Part B - Punkin Chunkin
Members of the World Championship Punkin Chunkin Association (WCPCA) (yes that is a thing!) come to Merrimack College to do a demonstration. The current world record is 4694.68feet horizontally. Assuming that record was set from a perfectly-horizontally deployed device, 10 feet off of the ground, and assuming no friction or wind resistance...
a. How long did it take the pumpkin to travel the world record distance [seconds]?
b. What was the world record pumpkin muzzle velocity [it/s]?
c. How far would that same "world record" pumpkin chunk go if it was made from the top of Mendel in feet? (i.e. it would go 4694.68feet horizontally if launched from 10 vertical feet off the ground, how far would it go horizontally if launched from 45 vertical feet off of the ground).
d. How far would the "world record" pumpkin go horizontally if it was shot perfectly-vertically at the "world record" muzzle velocity [ft]?
e. What is the maximum height that the "world record" pumpkin would reach in that case [ft]?
f. What is the time required for the vertically shot pumpkin to hit the ground [s]?
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