Projectile Motion: Calculating Vertical Component of Initial Velocity

What is the vertical component of the initial velocity when Ronnie kicks a playground ball with an initial velocity of 16 ft/s at an angle of 47 degrees? The vertical component of the initial velocity is approximately 10.99 ft/s.

Understanding Projectile Motion

Projectile motion is a crucial concept in physics that describes the motion of objects thrown or projected into the air. When an object is launched at an angle, its initial velocity can be split into two components: horizontal and vertical. Understanding these components is essential for analyzing how the object moves in both directions.

Calculating the Vertical Component

To find the vertical component of the initial velocity of Ronnie's playground ball, we can use trigonometry. The formula to calculate the vertical component is:

Vertical Component = Initial Velocity * sin(θ)

Given: - Initial Velocity = 16 ft/s - Angle (θ) = 47 degrees First, we need to convert the angle from degrees to radians:

θ = 47 degrees * (π / 180) ≈ 0.820 radians

Now, we can calculate the vertical component:

Vertical Component = 16 ft/s * sin(0.820 radians) ≈ 16 ft/s * 0.894 ≈ 10.99 ft/s

Therefore, the vertical component of the initial velocity is approximately 10.99 ft/s. This value represents the initial upward velocity of the ball when Ronnie kicked it.
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