Final answer:
To determine the vertical speed in projectile motion, resolve the initial velocity into vertical and horizontal components using trigonometric functions and apply kinematic equations considering gravity for changes in vertical velocity over time.
Step-by-step explanation:
To find the vertical speed in projectile motion, it is incorrect to simply multiply the horizontal speed by the time of flight or use only the vertical displacement divided by the time of flight. Instead, you resolve the initial velocity into horizontal and vertical components using trigonometric functions, generally sine and cosine. For an object projected at an angle θ, the initial vertical speed (vy) is given by vy = v sin(θ), where v is the magnitude of the initial velocity. If you need to find the vertical speed at a different time, you can use the kinematic equations considering the acceleration due to gravity affecting the vertical motion. The velocity in the vertical direction changes due to the acceleration of gravity. At the peak of the trajectory, the vertical velocity is zero. As the object descends, the vertical velocity increases in magnitude but points downwards, opposite to the initial direction if the motion is upward initially. These changes are captured by the equation vy = uy - gt, where uy is the initial vertical velocity, g is the acceleration due to gravity, and t is the time elapsed.