Adjustable Tennis Ball Launcher: Calculating Vertical Component of Initial Velocity

When dealing with projectiles launched at an angle, we need to consider both the horizontal and vertical components of the initial velocity. In this case, a tennis ball is launched with an initial velocity (Vi) of 8.0 meters per second at an angle of 50° above the horizontal. We are asked to find the vertical component of the ball's initial velocity.

To find the vertical component of the velocity, we can use trigonometry and the given information. The formula to find the vertical component of the velocity is: Vy = Vi * sin(theta), where Vy is the vertical component of the velocity, Vi is the initial velocity, and theta is the launch angle.

Plugging in the values given in the question:

Vy = 8.0 m/s * sin(50°)

Using a calculator, we can calculate that sin(50°) ≈ 0.766. Therefore, the vertical component of the ball's initial velocity is approximately:

Vy ≈ 8.0 m/s * 0.766 = 6.13 m/s

So, the vertical component of the ball's initial velocity is 6.13 m/s. This component represents the initial speed at which the ball is launched in the vertical direction, accounting for the angle at which it is launched.