A volleyball is spiked so that it has an initial velocity of 19.9 m/s directed downward at an angle of 55.8 ° below the horizontal. What is the horizontal component of the ball's velocity when the opposing player fields the ball?
To find the horizontal component of the volleyball's velocity, we need to use the trigonometric relationship between the angles and the sides of a right triangle.
The given angle, 55.8° below the horizontal, forms a right triangle with the horizontal and vertical components of the velocity. The horizontal component is what we are looking for, and the vertical component is the initial velocity of 19.9 m/s directed downward.
To find the horizontal component, we will use the cosine function, which relates the adjacent side (horizontal) to the hypotenuse (velocity).
cos(angle) = adjacent / hypotenuse
In this case, we have:
cos(55.8°) = horizontal component / 19.9 m/s
Now, we can rearrange the equation to solve for the horizontal component:
horizontal component = 19.9 m/s * cos(55.8°)
Using a scientific calculator, we find:
cos(55.8°) ≈ 0.5733
horizontal component ≈ 19.9 m/s * 0.5733
horizontal component ≈ 11.4 m/s
Therefore, the horizontal component of the ball's velocity when the opposing player fields the ball is approximately 11.4 m/s.