Final answer:
The horizontal velocity of a cannonball fired from a platform can be determined by first calculating the time of flight using the vertical distance it falls and gravity, then using that time to find velocity with the horizontal distance covered.
Step-by-step explanation:
To determine the horizontal velocity of a cannonball fired from a platform and landing a certain distance away, we first acknowledge that horizontal motion and vertical motion are independent of each other when air resistance is neglected. The horizontal velocity remains constant during the flight. The time of flight can be calculated using the vertical motion under gravity.
The vertical distance (s) the cannonball falls under gravity is given as 5 meters, with an initial vertical velocity (u) of 0 (since it is horizontally fired), and the acceleration due to gravity (g) as 9.8 m/s2. Using the formula s = ut + 0.5gt2, we calculate the time (t) of flight.
Once the time of flight is calculated, the horizontal velocity (v) is found using the horizontal distance (d) traveled, which is 62.6 meters, with the formula v = d/t. By solving for t and then v, we obtain one of the multiple-choice answers provided.