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The cannon on a pirate ships shoots cannon balls with a speed of 350 m/s (the muzzle velocity). The cannon can be adjusted to shoot at any elevation above the horizontal. The barrel is 2m long and the mass is 5 kg.

Ignoring air resistance and assuming the cannon ball is shot from ground (or water) level, what is the greatest horizontal distance the cannon ball can be shot?

What do I need to do to solve this? I know how to find the force and acceleration...

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3 answers
  1. put the barrel at 45 deg.
    find the time in air from the initial vertical velocity. Find the distance travealed from initial horizonal velocity and time in air.

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    bobpursley
  2. The greatest horizontal distance occurs at 45o.

    Vo = 350m/s[45o].
    Xo = 350*Cos45 = 247.5 m/s.
    Yo = 350*sin45 = 247.5 m/s.

    Y = Yo + g*Tr = 0,
    350 - 9.8*Tr == 0,
    Tr = 35.7 s. = Rise time.

    Tf = Tr = 35.7 s. = Fall time.

    T = Tr+Tf = 35.7 + 35.7 = 71.4 s. = Time in flight.

    d = Xo*T = 247.5 * 71.4 = Max horizontal distance.

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  3. Answer is 12495 m. Use vf= vi + a*t (to find time). Rise time and fall time will equal to 71.4 sec. Lastly, use d= vf+vi/2 * t --> d= 350/2 *71.4 --> 12,495 m

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