Detroit Tigers pitcher Joel Zumaya was recorded throwing a pitch at a velocity of 107 miles per hour.If he threw the pitch at an angle of 32° below the horizontal,find the vertical and horizontal components of the velocity.(Round your answers to one decimal place. )
A)Vertical ≈ -55.7 mi/h,Horisontal ≈ 91.7 mi/h.
B)Vertical ≈ 90.7 mi/h,Horisontal ≈ -56.7 mi/h.
C)Vertical ≈ -56.7 mi/h,Horisontal ≈ -56.7 mi/h.
D)Vertical ≈ -56.7 mi/h,Horisontal ≈ 90.7 mi/h.
E)Vertical ≈ 90.7 mi/h,Horisontal ≈ 90.7 mi/h.

Question

Detroit Tigers pitcher Joel Zumaya was recorded throwing a pitch at a velocity of 107 miles per hour.If he threw the pitch at an angle of 32° below the horizontal,find the vertical and horizontal components of the velocity.(Round your answers to one decimal place. ) ​
A)Vertical ≈ -55.7 mi/h,Horisontal ≈ 91.7 mi/h.
B)Vertical ≈ 90.7 mi/h,Horisontal ≈ -56.7 mi/h.
C)Vertical ≈ -56.7 mi/h,Horisontal ≈ -56.7 mi/h.
D)Vertical ≈ -56.7 mi/h,Horisontal ≈ 90.7 mi/h.
E)Vertical ≈ 90.7 mi/h,Horisontal ≈ 90.7 mi/h.

Quizplus · Accepted Answer

To find the vertical and horizontal components of the velocity, we use trigonometric functions. The horizontal component is found using $v \cos(\theta)$ and the vertical component using $v \sin(\theta)$, where $v$ is the velocity and $\theta$ is the angle. Given $v = 107$ mi/h and $\theta = 32^\circ$, the horizontal component is $107 \cos(32^\circ) \approx 90.7$ mi/h and the vertical component is $107 \sin(32^\circ) \approx 56.7$ mi/h. Since the pitch is below the horizontal, the vertical component is negative, making the correct answer $Vertical \approx -56.7$ mi/h, $Horizontal \approx 90.7$ mi/h.

Detroit Tigers Pitcher Joel Zumaya Was Recorded Throwing a Pitch