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Hobbyists build a compressed air powered cannon which is able to launch a pumpkin a horizontal...

Hobbyists build a compressed air powered cannon which is able to launch a pumpkin a horizontal distance of 4200 ft. Assuming no air resistance, and assuming the pumpkin is launched at ground level, what is the minimum initial speed of the pumpkin (just as it leaves the cannon) that is needed for it to reach this distance?

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Answer #1

Gravitational acceleration = g = 32.2 ft/s2

Horizontal range of the pumpkin = R = 4200 ft

Initial speed of the pumpkin = V

Angle of launch of the pumpkin =

The range for projectile motion is given by,

From this equation we can observe that for minimum speed the value of Sin(2) should be maximum.

The maximum value of Sine is 1.

Sin(2) = 1

V = 367.75 ft/s

Minimum initial speed of the pumpkin for it to reach this distance = 367.75 ft/s

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