Final answer:
To find the initial velocity of a cannon shell fired from a battleship, you would use the range formula of projectile motion, assuming no air resistance and a 45-degree launch angle. Solving the equation with the provided range of 32.0 km will yield the shell's initial velocity.
Step-by-step explanation:
Initial Velocity of Cannon Shell
To calculate the initial velocity of a cannon shell fired from a battleship, one would use the kinematic equations of projectile motion. Assume that the shell is fired at an angle that maximizes range, which is 45 degrees, and there is no air resistance. The range R of a projectile fired at a velocity v and an angle θ is given by the formula R = (v² ÷ g) × sin(2θ), where g is the acceleration due to gravity (9.81 m/s²). Since the maximum distance is 32.0 km (32000 m), we can solve for v:
R = (v² ÷ g) × sin(2θ)
32000 m = (v² ÷ 9.81 m/s²) × sin(90 degrees)
32000 m = (v² ÷ 9.81 m/s²)
v = sqrt(32000 m × 9.81 m/s²)
After solving for v in the above equation, you would find the initial velocity of the cannon shell.