To determine the greatest kinetic energy the cannonball can have when it hits its target, we need to consider the relationship between kinetic energy and speed. The kinetic energy (K) of an object can be calculated using the formula:
K = (1/2)mv^2
Where:
K = kinetic energy
m = mass of the object
v = velocity of the object
In this case, we are given the muzzle velocity (v) of the cannonball, but we need to determine its mass (m). Since the mass of the cannonball is not provided, we can't calculate the exact kinetic energy.
However, we can make use of the fact that the kinetic energy is directly proportional to the square of the velocity. This means that if we compare two different velocities, the ratio of their kinetic energies will be equal to the square of the ratio of their velocities.
Since the target is at the same height above the ground as the cannon, the cannonball will have the highest kinetic energy when it is shot horizontally (at an elevation angle of 0 degrees). In this case, the vertical component of the velocity is zero, and only the horizontal component contributes to the kinetic energy.
Therefore, the greatest kinetic energy of the cannonball can be calculated by squaring the muzzle velocity and using it as an approximation. To find the kinetic energy, we need to square the muzzle velocity (350 m/s) and multiply it by half of the mass of the cannonball.
However, since we don't have the mass, we can't provide a numerical value for the greatest kinetic energy.