Question

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...

Answer 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.

Answer 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.

Answer 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

Answer 4

Acceleration and Force?

Answer 5

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.