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...

5 answers

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.
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.
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
Acceleration and Force?
the time of flight will be calculated as follows
v=u+at
0 = 350 * cos(45 deg) - 9.8 * t
t = 350/ ((sqrt 2) * 9.8)
t = 25.25 sec
Total flight time = Rise time + Fall time = 2 * 25.25 = 50.5
Horizontal distance = Speed * time
350 * sin(45 deg) * 50.5
10897m = Max Horizontal Distance traveled.