Question

Punkin Chunkin In Sussex County, Delaware, a post- Halloween tradition is "Punkin Chunkin," in which contestants build cannons, catapults, trebuchets, and other devices to launch pumpkins and compete for the greatest distance. Though hard to believe, pumpkins have been projected a distance of 4086 feet in this contest. What is the minimum initial speed needed for such a shot?

Answer 1

for maximum range of pumpkins we can say

$R = \frac{v^2 sin2\theta}{g}$

here angle must be 45 degree for maximum range

$4086 = \frac{v^2 sin(2*45)}{32.2}$

$v = 362.7 ft/s$

$v =110.6 m/s$

Answer 2

R_max = v²/g =4086ft =4086*(12*0.0254)= v²/9.81m/s²

therefore, v= 110.53 m/s or 362.63 ft/sec

Answer 3

Range = R = u^2*sin(2x)/g = 4086 ft

g = 32.17 ft/m^2

Minimum speed , x = 45

So

u = sqrt(g*4086)

u = sqrt(32.17*4086) = 362.55 ft/s

minimum initial speed needed for such a shot = 362.55 ft/s