Final answer:
To find the basketball's initial velocity, we subtract the initial velocity from the final using vector subtraction, but we need additional data such as horizontal velocity or time of flight. The Pythagorean theorem gives us the magnitude of velocity if horizontal and vertical components are known.
Step-by-step explanation:
To determine the magnitude va of the basketball's initial velocity, we must consider the final velocity and the change in velocity. The change in velocity, ΔV, is calculated by vector subtraction: ΔV = Vf - Vi, where Vf is the final velocity and Vi is the initial velocity. Since we're told that the ball moves along a straight line, the algebraic method is appropriate.
Given the vertical component of the final velocity, Vy = -24.5 m/s, and assuming we have a horizontal component (presumably provided in the question but omitted here), we can find the magnitude of the final velocity v using the Pythagorean theorem, v = √(vx² + vy²). However, to solve for the initial velocity, additional information is required. Typically, we would use kinematics equations, taking into account initial and final velocities, acceleration (due to gravity if the ball is being thrown), and the distance traveled.