what is the minimum initial speed of the pumpkin (just as it leaves the cannon) that is needed for it to reach this distance?

Hobbyists build a compressed air powered cannon which is able to launch a pumpkin a horizontal distance of 3600 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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  • 5 years ago
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    when a projectile comes back to the same height as that from which it was fired

    this is the range equation

    R = (Vo^2 / g) sin 2 θ

    without using too much complicated math

    we can see that for any given Vo the max R will be when sin 2 θ is also max

    and the max value of sin is 1

    so sin 2 θ = 1 gives 2 θ = 90 and θ = 45

    now we can go back and find the Vo at 45°, the optimal angle

    3600 = Vo^2 / 32.2 (1)

    Vo^2 = 115920

    Vo = 340.5 ft/s

    round appropriately

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