Questions: A pool player located at X wants to shoot the white ball off the top cushion and hit the red ball dead center. He knows from physics that the white ball will come off a cushion at the same angle as that at which it hit the cushion. If the deflection angle, θ, is 47°, where on the top cushion should he hit the white ball? The white ball should hit the top cushion approximately from the top left comer. (Round to two decimal places as needed.)

A pool player located at X wants to shoot the white ball off the top cushion and hit the red ball dead center. He knows from physics that the white ball will come off a cushion at the same angle as that at which it hit the cushion. If the deflection angle, θ, is 47°, where on the top cushion should he hit the white ball?

The white ball should hit the top cushion approximately from the top left comer. (Round to two decimal places as needed.)
Transcript text: A pool player located at $X$ wants to shoot the white ball off the top cushion and hit the red ball dead center. He knows from physics that the white ball will come off a cushion at the same angle as that at which it hit the cushion. If the deflection angle, $\theta$, is $47^{\circ}$, where on the top cushion should he hit the white ball? The white ball should hit the top cushion approximately $\square$ $\square$ from the top left comer. (Round to two decimal places as needed.)
failed

Solution

failed
failed

Solution Steps

Step 1: Find the angle of incidence

The angle of incidence is equal to half the deflection angle. Since the deflection angle is 47°, the angle of incidence is 47°/2 = 23.5°.

Step 2: Set up a trigonometric equation

Let 'd' be the distance from the top left corner to where the white ball should hit the top cushion. We can use the tangent function to relate the distance 'd', the angle of incidence (23.5°), and the vertical distance from the white ball to the top cushion (3 ft). The equation is: tan(23.5°) = d / 3

Step 3: Solve for d

Multiplying both sides of the equation by 3, we get: d = 3 * tan(23.5°) ≈ 3 * 0.4348 ≈ 1.3044 ft

Final Answer: The white ball should hit the top cushion approximately 1.30 ft from the top left corner.

Was this solution helpful?
failed
Unhelpful
failed
Helpful