A soccer goalkeeper takes a goal kick and the ball leaves his foot with a vertical velocity of 15 m/s and a horizontal velocity of 25 m/s. What is the angle of the resultant velocity vector from the horizontal?
Question
A soccer goalkeeper takes a goal kick and the ball leaves his foot with a vertical velocity of 15 m/s and a horizontal velocity of 25 m/s. What is the angle of the resultant velocity vector from the horizontal?
Solution
To find the angle of the resultant velocity vector from the horizontal, we can use the formula for the tangent of the angle, which is the vertical velocity divided by the horizontal velocity.
Step 1: Identify the given values. Vertical velocity (Vy) = 15 m/s Horizontal velocity (Vx) = 25 m/s
Step 2: Use the formula for tangent. tan(θ) = Vy / Vx
Step 3: Substitute the given values into the formula. tan(θ) = 15 m/s / 25 m/s
Step 4: Calculate the tangent. tan(θ) = 0.6
Step 5: Find the angle by taking the inverse tangent (also known as the arctangent) of the result. θ = arctan(0.6)
Step 6: Use a calculator to find the arctangent of 0.6. θ = 30.96 degrees
So, the angle of the resultant velocity vector from the horizontal is approximately 31 degrees.
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