On a pool table, where along the potion of CD of the railing should you direct ball A so that it will bounce off CD and strike ball B? Assume that A obeys the law of reflection relative to the rail CD.
AC= 15
CD= 30
BD= 10
make a line graph of the data. use a scales from 0to600 and an interval of 100 for the population. write a sentence about the trend show on the graph.
want huoii
To determine where along the portion CD of the railing you should direct ball A in order to strike ball B, you need to make use of the law of reflection.
Here's how you can approach the problem:
1. Draw a diagram: Sketch a pool table with the given measurements. Label points A, B, C, and D as specified in the question, and mark the distances AC = 15 units, CD = 30 units, and BD = 10 units. This will help you visualize the situation.
2. Understand the law of reflection: According to the law of reflection, the angle of incidence (the angle at which ball A approaches the railing) is equal to the angle of reflection (the angle at which ball A bounces off the railing). This law applies when the ball strikes the railing perpendicularly.
3. Find the angle of incidence: To calculate the angle of incidence, you need to consider right triangle ADC, formed by points A, D, and C. The length of AD is the sum of AC and CD, which means AD = AC + CD = 15 + 30 = 45 units. You can use the Pythagorean theorem to find the length of DC: DC² = AD² - AC². Substituting the values: DC² = 45² - 15² = 2025 - 225 = 1800. Taking the square root of both sides, you get DC ≈ √1800 ≈ 42.43 units.
4. Calculate the angle of incidence: You can determine the angle of incidence by considering triangle BCD, formed by points B, C, and D. As triangle BCD is a right triangle, you can use trigonometry to calculate the angle of incidence. The tangent of the angle of incidence (θ) is equal to the length of the opposite side (BD = 10 units) divided by the adjacent side (DC ≈ 42.43 units). Therefore, tan(θ) ≈ BD / DC = 10 / 42.43 ≈ 0.236. Using a trigonometric calculator or inverse tangent (arctan) function, you can find that the angle of incidence (θ) is approximately 13.53 degrees.
5. Determine the angle of reflection: Since the angle of reflection is equal to the angle of incidence, the angle of reflection is also approximately 13.53 degrees.
6. Mark the spot to direct ball A: Measure 13.53 degrees from the perpendicular line CD and mark the point where the extension of the line from point A intersects CD. This is the point on the railing where you should direct ball A so that it will bounce off CD and strike ball B.
Remember, the above steps provide a general approach to solve the problem. In practice, you may need to consider factors such as the shape of the pool table rails, the elasticity of the balls, and any potential friction to achieve the desired outcome accurately.