A volleyball is spiked so that it has an initial velocity of 14 m/s directed downward at an angle of 61° below the horizontal. What is the horizontal component of the ball's velocity when the opposing player fields the ball?
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To find the horizontal component of the ball's velocity, we first need to break the initial velocity into its horizontal and vertical components.
Given:
Initial velocity magnitude (v₀) = 14 m/s
Angle below the horizontal (θ) = 61°
To find the horizontal component (vₓ) of the velocity, we use the formula:
vₓ = v₀ * cos(θ)
Substituting the given values into the formula:
vₓ = 14 m/s * cos(61°)
To calculate the horizontal component, follow these steps:
Step 1: Convert the angle from degrees to radians.
θ (in radians) = 61° * (π/180°)
Step 2: Use the cosine function to find the horizontal component.
vₓ = 14 m/s * cos(61° * (π/180°))
Evaluating the expression will give us the horizontal component of the velocity.