The cannon on a pirate ships shoots cannon balls with a speed of 350m/s (the muzzle velocity). The cannon can be adjusted to shoot at any elevation above the horizontal.

Question

What is the greatest kinetic energy the cannon ball can have when it hits its target in J? Ignore air resistance and assume the target is at the same height above the ground (or water) as the cannon.

Answer 1

The greatest kinetic energy the cannon ball can have when it hits its target will be when it is fired directly at the target, or at a 90-degree angle to the ground.

We can use the kinetic energy formula, KE = 0.5 * m * v^2, to calculate the maximum kinetic energy of the cannon ball.

Assuming the cannon ball has a mass of 10 kg (a typical weight for a cannon ball), we can plug in the given muzzle velocity of 350 m/s:

KE = 0.5 * 10 kg * (350 m/s)^2 = 6.125 * 10^6 J

So the greatest kinetic energy the cannon ball can have when it hits its target is approximately 6.125 million joules.

Answer 2

Since the cannon and the target are at the same height there is no change in potential energy between start and finish.
Therefore there is no change in kinetic energy as well between start and finish since the no energy is lost or gained during the flight.
(1/2) m v^2 = (1/2) * 5 * 350^2 = 306250 Joules

Answer 3

You are correct. If there is no change in height between the cannon and target, then there is no change in potential energy and therefore the maximum kinetic energy the cannon ball can have when it hits the target is equal to the initial kinetic energy of the cannon ball.

Using the formula KE = 0.5 * m * v^2 with a mass of 5 kg (typical weight for a cannon ball) and a muzzle velocity of 350 m/s, we get:

KE = 0.5 * 5 kg * (350 m/s)^2 = 306,250 J

Therefore, the maximum kinetic energy the cannon ball can have when it hits the target is approximately 306,250 joules.