MATHEMATICS MIDDLE SCHOOL

A billiard ball is struck by a cue. It travels 100\,\text{cm}100cm100, start text, c, m, end text before ricocheting off a rail and traveling another 120\, \text{cm}120cm120, start text, c, m, end text into a corner pocket. The angle between the path as the ball approaches the rail and the path after it strikes the rail is 45^{\circ}45 ∘ 45, degrees. How far is the corner pocket from where the cue initially struck the ball?

Answers

Answer 1

Answer:

Answer:

$\large \boxed{\text{86 cm}}$

Step-by-step explanation:

I think what you are saying is represented by the diagram below.

The ball starts at A, rebounds from the far wall at a 45° angle and into the corner pocket at C.

You want the find the distance from A to C.

We can use the Law of Cosines to answer this question

$\begin{array}{rcl}b^(2) & = & a^(2) + c^(2) - 2ac\cos \theta\n& = & 120^(2) + 100^(2) - 2 *120*100 * \cos 45^(\circ)\n& = & 14400 + 10000 - 24000*0.7071\n& = & 24400 - 16971\n& = & 7429\n b & = & \textbf{86 cm}\n\end{array}\n\text{The corner pocket is $\large \boxed{\textbf{86 cm}}$ from where the cue originally struck the ball.}$

Answer 2

Answer:

Answer:

about 86 cm

Step-by-step explanation:

My understanding of the geometry is shown in the attached figure.

Since the angle of incidence is equal to the angle of reflection, the angle APP₂ will be 22.5°, and the vertical distance from the pocket P to the ball position B is ...

(PA +AB')sin(22.5°) = 220sin(22.5°) ≈ 84.19 . . . . cm

The horizontal distance PB is

(PA -AB)cos(22.5°) = 20cos(22.5°) ≈ 18.48 . . . . . cm

The distance PB is given by the distance formula ...

PB = √(84.19² +18.48²) ≈ 86.19 . . . . cm

The ball was initially about 86 cm from the corner pocket.

Related Questions

(05.01)How many solutions will this system of equations have? (2 points)x − 2y = 243x − 6y = 72Select one:a. No solutionb. Infinite solutionsc. One solutiond. Two solutions
Evaluate each function rule. Find y for x=0, 1, 2, and 3. Construct a function table for each problem.y=3x+1
Whats the differance between pount and lbs ?
How do you convert 2/30 into a percent ?
Which completely describes the polygon A. equilateral B. equiangular C. regular btw the figure polygon is a sqaure

HELP please ASAP pls...

Answers

The answer is: -28/5

Hope this helps!!!!!!!

Evaluate the expression
-112/7+9

Answers

-112/7+63/7 = -49/7 = -7

The price of a tent was decreased by 15% and sold for $76.49. What was the original price of the tent in dollars?

Answers

$(0.100-0.15)x=76.49$

$0.85x=76.49$

$x= (76.49)/(0.85)$

$x=89.99$

$$89.99$

Answer:

89.99

Step-by-step explanation:

What is 26/39 in its simplest form

Answers

To write a fraction in simplest form, first we need to find the Greatest Common Factor (or GCF) of the numerator and the denominator.

The GCF of 26 and 39 is 13.

Therefore, we should divide both the numerator and the denominator by this number.

26 / 13 = 2

39 / 13 = 3

Therefore, 2/3 is 26/39 in simplest form.

The cable company charges $30 to install new supplies at your house. Each month the cable bill is $75. Which equation models the total cost for cable over time?

Answers

The correct answer is:

D. y=75x+30

Equation: $30+$75m
M=per month

Find the slope of the parallel to each given line.1) y=2/3x-2
2)y=9/5x-5

Find the slope of a line perpendicular to each given line

1)y=-1/2x-2
2)y=-x-1

Answers

Slopes of parallel lines are same, only the y-intercepts are different

Slopes of perpendicular lines are opposite reciprocals, which means when they are multiplied, it equals to -1.

1)
Parallel lines have the same slopes
y=mx+b where m is the slope

so the slope of a parallel line would be 2/3

2)
y=9/5x -5
slope will be 9/5

Next set of questions:

1) y=-1/2x - 2

$-(1)/(2) * x = -1 \to x = 2$

So that means the slope is 2

2) y=-x-1
Slope is -1, and we need to find the slope for a line perpendicular to it.

$-1 * x = -1 \to x=1$

So the slope is 1

Other Questions

Which system of inequalities has a solution set that is a line?[x+y23[x+y s3[x+y2-3Extysa0[x+y>3(x + y <3(x+y> -3(x+y<3

Hey idk what 2+2 is

What is the sum of an infinite geometric series if a1 = 5 and r = 1/3

X+ 1/x =5 what is the value x²+1/x²?