Final answer:
To calculate the actual velocity of a projectile, use the equation v = u + at. To calculate the theoretical velocity, use the equation v = √(v_x^2 + v_y^2).
Step-by-step explanation:
The actual velocity and theoretical velocity of a projectile can be calculated using the given height and time. To find the actual velocity, we need to know the horizontal and vertical components of the velocity. The horizontal velocity remains constant throughout the motion, while the vertical velocity changes due to the acceleration due to gravity. By using the equation v = u + at, where u is the initial velocity and a is the acceleration, we can determine the vertical velocity at any given time. To find the theoretical velocity, we can use the equation v = √(v_x^2 + v_y^2), where v_x is the horizontal velocity and v_y is the vertical velocity. By substituting the horizontal and vertical velocities into this equation, we can calculate the theoretical velocity of the projectile.