A player located 18.6 ft from the basket launches a successful jump shot from a height of 10 ft (level with the rim of the basket), at an angle = 36 and an initial velocity of v = 25 ft/s. Find the change of distance s of the toss if the angle changes by an amount . Hint: Use the following fact derived from Newton's Laws: An object released at an angle with initial velocity v ft/s travels a total distance [tex]s=\frac{1}{32} v^{2} sin(2\theta)[/tex]

Mathematics High School

A player located 18.6 ft from the basket launches a successful jump shot from a height of 10 ft (level with the rim of the basket), at an angle θ = 36º and an initial velocity of v = 25 ft/s. Find the change of distance Δs of the toss if the angle changes by an amount Δθ. Hint: Use the following fact derived from Newton's Laws: An object released at an angle θ with initial velocity v ft/s travels a total distance [tex]s=\frac{1}{32} v^{2} sin(2\theta)[/tex]

Answers

Answer 1

Answer:

Step-by-step explanation:

You suck free points

Answer 2

The change of the distance travelled by the ball when the angle of launch

changes can be found by linear approximation.

The change in the distance, Δs, when the angle changes by Δθ in radians is approximately 0.211·Δθ.

Reasons:

The distance of the player from the basket = 18.6 ft.

Height from which the jump shot is launched = 10 ft.

Angle of the jump shot = 36°

The initial velocity = 25 ft./s

According to Newton's Law of motion, the distance an object travels when

released at an angle θ, with an initial velocity, v, is given by the following

horizontal range formula equation;

[tex]s = \dfrac{1}{32} \cdot v^2 \cdot sin(2 \cdot \theta)[/tex]

[tex]\dfrac{ds}{d\theta} =\dfrac{d}{d\theta } \left( \dfrac{1}{32} \cdot v^2 \cdot sin(2 \cdot \theta) \right)= \dfrac{v^2 \cdot cos(2 \cdot \theta)}{16}[/tex]

By linear approximation, we have;

[tex]\Delta s = \dfrac{ds}{d\theta} \times \Delta \theta[/tex]

Which gives;

[tex]\Delta s =\dfrac{25^2 \cdot cos(2 \times 36^{\circ})}{16}\times \Delta \theta \approx 12.07 \times \Delta \theta[/tex]

360° = 2·π radians

[tex]12.07 ^{\circ} = \dfrac{2 \cdot \pi}{360} \times 12.07 \approx 0.211 \ radians[/tex]

Δs ≈ 0.211·Δθ

Therefore;

The change in the distance, Δs, when the angle changes by Δθ is 0.211·Δθ.

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Related Questions

Write the equation of the line, in slope-intercept form, with the
following information:
slope: -2
point: (5,-4)

Answers

Answer:

Step-by-step explanation:

y + 4 = -2(x - 5)

y + 4 = -2x + 10

y = -2x + 6

HELPPPP plzz!!

A.) Side - Side - Side
B.) Side - Angle - Side
C.) Angle - Side - Angle
D.) Angle - Angle - Side
E.) Hypotenuse - Leg

Answers

Oh wait I think I know the answer, c.

Answer:

Step-by-step explanation:

angle DAB = angle CBA

angle DBA = angle CAB

line AB = line AB

Since we know that the two angles and 1 side are the same on both triangle ADB and BCA, the property is angle side angle

In 2003, the average attendance per game for a football team was about (1 × 104) + (9 × 103) + (9 × 102). What is this number in standard form?

show work

Answers

Answer:

1.99 * 10^4

Step-by-step explanation:

Here, we want to write the addition in standard form

= (1 * 10^4) + (9 * 10^3) + (9 * 10^2)

= 10,000 + 9000 + 900

= 19,900

so the number in standard form is;

1.99 * 10^4

I have 1373/1000 Points, and 10/10 brainiest. Why am I not leveling up to Expert?

Answers

Answer:

some thing is broken man

Step-by-step explanation:

Translation of, “Six less than twice the value of x,”.

Answers

Answer:

2x-6

Step-by-step explanation:

Which expression has a value of 8?
1. 720 divided by 9
2. 720 divided by 90
3. 7200 divided by 9
4. 7200 divided by 90

Answers

Answer:

720 divided by 90

Step-by-step explanation:

72 divided by 9 is 8. 720 divided by 9 is 80 because you're keeping the 0, but when dividing, take away the zeros if both numbers have a zero to make it easier

A pebble is dropped into a deep well and 3s later the sound of a splash is heard as the pebble reaches the bottom of the well. The speed of sound in air is about 340 m/s. How long will it take fir the pebble to hit the water? How long does is take for the sound to reach the observer? What is the depth of the well? (I need the equation)

Answers

Answer:

[tex]2.89\ \text{s}[/tex]

0.11 seconds

[tex]37.4\ \text{m}[/tex]

Step-by-step explanation:

[tex]t_1[/tex] = Time taken by the pebble to hit the water

[tex]t_2[/tex] = Time taken by the sound to travel to the observer

[tex]t_1+t_2[/tex] = Time taken by the observer to listen to the splash after stone is thrown = 3 s

[tex]t_1=3-t_2[/tex]

a = g = Acceleration due to gravity = [tex]9.81\ \text{m/s}^2[/tex]

[tex]u_s[/tex] = Speed of sound = 340 m/s

The distance traveled by the pebble

[tex]s=ut+\dfrac{1}{2}at_1^2\\\Rightarrow s=0+\dfrac{1}{2}\times9.81(3-t_2)^2\\\Rightarrow s=4.905(9+t_2^2-6t_2^2)[/tex]

Distance traveled by the sound

[tex]s=u_st\\\Rightarrow s=340\times t_2[/tex]

The distance traveled by the sound and the pebble is equal

[tex]4.905(9+t_2^2-6t_2)=340\times t_2\\\Rightarrow 9+t_2^2-6t_2=\dfrac{340}{4.905}t_2\\\Rightarrow 9+t_2^2-6t_2=69.32t_2\\\Rightarrow t_2^2-75.32t_2+9=0\\\Rightarrow t_2=\frac{-\left(-75.32\right)\pm \sqrt{\left(-75.32\right)^2-4\times \:1\times \:9}}{2\times \:1}\\\Rightarrow t_2=75.2,0.11[/tex]

Since [tex]t_1+t_2=3[/tex] the value of [tex]t_2[/tex] cannot be greater than 3.

So, time taken by the sound to reach the observer is 0.11 seconds.

Time taken by the pebble to hit the water is [tex]t_1=3-t_2=3-0.11=2.89\ \text{s}[/tex]

Depth of the well is [tex]s=340t_2=340\times 0.11=37.4\ \text{m}[/tex]

4. x =
a. 20°
b. 240
C. 28°
(5x)
120°
d. 30°

Answers

An exterior angle equals the sun of the two opposite inside angles:

5x = 120 + x

Subtract 1 x from both sides:

4x = 120

Divide both sides by 4:

X = 30

The answer is D. 30

What is the equation of this graphed line?
Enter your answer in slope-intercept form.

Please answer quickly, I will give brainliest to whoever answers correctly, thank you.

Answers

Answer:

y = -9/8x + 7

Step-by-step explanation:

Slope-intercept form is:

y = mx + b

Points given:

(0, 7) and (8, -2)

y-intercept is

b = 7 as per the first point

And the slope is:

m = (-2 - 7)/(8 - 0) = -9/8

So the line is:

y = -9/8x + 7

Answer:

Required Answer:-

points are

(0,7)(8,-2)

slope =m

[tex]{:}\longrightarrow[/tex][tex]\sf m={\dfrac {y_2-y_1}{x_2-x_1}}[/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf {\dfrax {-2-7}{8-0}}[/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf {\dfrac {-9}{8}}[/tex]

y intercept:-

Hence the equation is

[tex]{:}\longrightarrow[/tex][tex]\sf y={\dfrac {-9}{8}}+7 [/tex]

It says I have 13 free answers left and then it says I used them all so I only get 2 free. why?

Answers

Answer: That used to happen to me but if you answer peoples questions it doesnt do that anymore because you are helping out

Step-by-step explanation:

Answer:

you have to use ads wich is stupid

Step-by-step explanation:

what is any of these questions dont worry bout the others

Answers

Answer:

All that u hav to do is 2 apply BODMAS rule. And it will be done. thanq

Step-by-step explanation:

HEEEEEEEEEEEEEEELLLLLLLPPPPP PLEASE

Answers

Answer:

3 1/5

Step-by-step explanation:

I used my calculator, but convert to the greatest common factor which is 15 and multiply, then simplify to 16/5 and turn to a proper fraction 3 1/5.

Answer:

= 16/5 = 3 1/5

Step-by-step explanation:

A train freight car weighs 25 tons when empty. A conveyor belt pours coal into the car at a constant rate of 1/3 ton per minute until it is full.

The dump truck (Refer to problem 8) weighs 55 tons when filled. At the same time the freight car is being filled, an identical freight car filled

to capacity is being emptied at a rate of 1/6 ton per minute.

How long, in minutes, until the freight cars are the same weight?

The tucks will weigh the same in

minutes.

How much coal will be in each truck when they weigh the same?

There will be

tons of coal in each truck.

Answers

Step-by-step explanation:

Step one:

mass of Freight car=25tons

the rate of filling is 1/3 ton per minute

let the time taken to fill the freight car be x

and the total mass after x minute be y

Hence the mass as a function of time is expressed as

y=25+1/3x----------1

mas of dump truck=55tons

rate of being emptied= 1/6 tons per minute

let the time taken to empty the dump truck be x

and the total mass after x minute be y

Hence the mass as a function of time is expressed as

y=55-1/6x----------2

Step two:

equating equations 1 and 2,

1. The tucks will weigh the same in

55-1/6x=25+1/3x

collect like terms

55-25=1/3x+1/6x

30=(2+1/6)x

30=3/6x

30=1/2x

30=0.5x

x=30/0.5

x=60min

1 hour

The tucks will weigh the same in 60minutes(1 hour)

2. How much coal will be in each truck when they weigh the same?

For the train freight car, the weight after 60 minutes is

y=25+1/3(60)

y=25+20

y=55tons

55-25=20tons

There will be 20tons

For the dump truck, the weight after 60 minutes is

y=55-1/6(60)

y=55-10

y=45tons

55-45=10tons

There will be 10tons

x + 2x + (-24)
How do I do this

Answers

Answer:

Since it is not an equation you would combine like terms and the answer would be 3x + (-24)

Step-by-step explanation:

There is no answer technically, you're just simplifying

Answer:

Step-by-step explanation:

you can't solve you don't know what X is so x+ 2x + (-24) is the answer

If m = 50, what is the value of the expression below?

0.44m + 23

A. 22
B. 45
C. 67
D. 117

SHOW YOUR WORK PLZSSSSSSSS

Answers

Answer:

B. is your answer dear

Step-by-step explanation:

0.44*50+23

22+23 = 45

hope you got it.

Help me Please
The boy scouts are selling popcorn for $25 a bag. They have already sold $525 worth and want to make at least $5750. Write an inequality to find the least number of bags of popcorn they need to sell to reach their goal. How many bags is that?

Answers

Answer:

B ≥ 209

Step-by-step explanation:

This is the equation - 25b + 525 ≥ 5750 .

Comment if I solved it incorrectly ;-;

Lucia invests $5000 at a rate of 4.5% per year compound interest. Calculate the value of her investment at the end of 7 years.

Answers

The value of her investment at the end of 7 years is $11804

How to determine the value?

The given parameters are

Principal, P = $5000

Rate, r = 4.5%

Time, t = 7 years

The value is then calculated as:

Value = P * P(1 + r)^t

So, we have:

Value = 5000 + 5000 * (1 + 4.5%)^7

Evaluate the expression

Value = 11804

Hence, the value of her investment at the end of 7 years is $11804

Read more about compound interest at:

https://brainly.com/question/24924853

#SPJ1

Find the value of x in the triangle below.

x = ?

Answers

Answer:

x=8

Step-by-step explanation:

hope i helped!!!

Answer:

61°

Step-by-step explanation:

180-58=122

122÷2=61

27 : 18 = 13 : x find x

Answers

Answer: 27:18 and 13:x can also be written as 27/18 and 13/x

therefore, 27:18 = 13:x

27/18 = 13/x

27/18 *13= x

x = 19.5

Hope it helped u,

pls mark as the brainliest

and put thanks

^_^

3. Multiply and simplify: (4x + 3)(x - 1)
Answer =

Answers

4x^2-x-3 is the correct answer:)

Answer: = 4x² - x - 3

(4x+3)(x -1 ) = 4x² + 3x - 4x - 3 = 4x² - x - 3

Step-by-step explanation:

Write as a product:
a2+b2–2ab –25

Answers

Answer: -a2 - 2ab - b2 + 25 =

-1 • (a2 + 2ab + b2 - 25)

Final result :

-a2 - 2ab - b2 + 25

Step-by-step explanation:

Dan made $5.38 for a half hour of work. At Dan's current rate of pay, how much would Dan make for 8 hours of work?

Answers

Answer:

The answer is 86.08, hope this helps.

Step-by-step explanation:

Answer:

$86.08

Step-by-step explanation:

If Dan makes $5.38 for HALF an hour how much does he make for a full hour? He makes $10.76 for an entire hour.

$10.76 x 8= $86.08

please helpp mecwith this question

Answers

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[tex] \frac{1}{R} = \frac{1}{8} + \frac{1}{12} \\ [/tex]

[tex] \frac{1}{R} = \frac{1 \times 3}{8 \times 3} + \frac{1 \times 2}{12 \times 2} \\ [/tex]

[tex] \frac{1}{R} = \frac{3}{24} + \frac{2}{24} \\ [/tex]

[tex] \frac{1}{R} = \frac{3 + 2}{24} \\ [/tex]

[tex] \frac{1}{R} = \frac{5}{24} \\ [/tex]

Inverse both sides

[tex] \frac{R}{1} = \frac{24}{5} \\ [/tex]

[tex]R = \frac{24 \times 2}{5 \times 2} \\ [/tex]

[tex]R = \frac{48}{10} \\ [/tex]

[tex]R = 4.8 \: \: Ω[/tex]

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The correct answer is (( B )) .

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i need this asap!!!! please! will give brainliest and a thanks to fast answers!

Answers

Answer:

2 big

30 small

Step-by-step explanation:

possibility

Answer: 2 big
30 small

How long can you hold your breath? A statistical question or nonstatistical question

Answers

Answer:

nonstatistical

Step-by-step explanation:

Have a great day and hope this helps

Answer:

statistical

Step-by-step explanation:

i did it

A telephone pole is 24 feet tall. A support cable is attached to the top of the pole to keep the pole from leaning. The stake for the cable is set in the ground 18 feet away from the base of the pole, as shown. How long is the support cable?

Answers

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

the functions f(x), g(x), and h(x), find the average rate of change over the interval -3≤x≤5

Answers

The average is you can search for it online. X

solve for x : 4 (1 - x) + 2x = -3 (x+1)

Answers

Answer: x=-7

Step-by-step explanation:

Please answer these series of questions! I will give high points and brainliest!

A. Reduce 3/51 to its simplest terms

B. Solve 7 divided by 3 (in fractions!)

C. 19 divided by 3 (fractions)

D. Reduce 50/80 to simplest terms

E. Reduce 9/14 to simplest terms

F. Reduce 36/54 to simplest terms

G. Solve 55 divided by 12 (fractions)

H. Reduce 9/153 to simplest terms

That’s all! ( please answer correct my life is depending on it, my mom will literally beat me up )

Answers

Answer:

A: 1/17 or decimal form: 0.058

B: 7/3 or mixed #: 2 1/3

C: 19/3 or mixed #: 6 1/3

D: 5/8

E: 9/14

F:2/3

G: 55/12 or mixed #: 4 7/12

H: 1/17

Step-by-step explanation:

Pls help with this question

Answers

Answer:

Opposite sides are congruent

Step-by-step explanation:

First off the equals sign with the wave over it means congruent. It wouldn't be either answer with diagonals because the segments that are congruent are sides of the parallelogram not diagonals. Next even though the congruent sides are parallel by providing the information (AB being congruent to CD and AD bring congruent to CB) opposite are parallel wouldn't be the answer because of what you are given.

Sorry if its wordy I hope this helps : )

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