Doug hits a baseball straight towards a 15 ft high fence that is 400 ft from home plate. The ball is hit 2.5ft above the ground and leaves the bat at an angle of 30∘ with the horizontal. Find the minimum initial velocity needed for the ball to clear the fence.

Answers

Answer 1

Answer:

[tex]125.4\ \text{m/s}[/tex]

Step-by-step explanation:

u = Initial velocity of baseball

[tex]\theta[/tex] = Angle of hit = [tex]30^{\circ}[/tex]

x = Displacement in x direction = 400 ft

y = Displacement in y direction = 15 ft

[tex]y_0[/tex] = Height of hit = 2.5 ft

[tex]a_y[/tex] = g = Acceleration due to gravity = [tex]32.2\ \text{ft/s}^2[/tex]

t = Time taken

Displacement in x direction

[tex]x=u_xt\\\Rightarrow x=u\cos\theta t\\\Rightarrow t=\dfrac{x}{u\cos\theta}\\\Rightarrow t=\dfrac{400}{u\cos30^{\circ}}\\\Rightarrow t=\dfrac{400}{u\dfrac{\sqrt{3}}{2}}\\\Rightarrow t=\dfrac{800}{u\sqrt{3}}[/tex]

Displacement in y direction

[tex]y=y_0+u_yt+\dfrac{1}{2}a_yt^2\\\Rightarrow y=y_0+u\sin\theta t+\dfrac{1}{2}a_yt^2\\\Rightarrow 15=2.5+u\sin30^{\circ}(\dfrac{800}{u\sqrt{3}})+\dfrac{1}{2}\times -32.2\times (\dfrac{800}{u\sqrt{3}})^2\\\Rightarrow \dfrac{400}{\sqrt{3}}-\dfrac{10304000}{3u^2}-12.5=0\\\Rightarrow 218.44=\dfrac{10304000}{3u^2}\\\Rightarrow u=\sqrt{\dfrac{10304000}{3\times218.44}}\\\Rightarrow u=125.4\ \text{m/s}[/tex]

The minimum initial velocity needed for the ball to clear the fence is [tex]125.4\ \text{m/s}[/tex]


Related Questions

Image by Scientif3
Name all of the obtuse angles that share a side with ZVON.
A. ZNOS, ZNOP, ZNOQ, VOS, ZV00, ZVOP
B. ZNOS, ZNOT, ZNOV, ZVOR, ZVOU, ZVOP
C. ZNOS, ZNOT, ZNOR, ZVOR, ZVOQ, ZVOP
D. ZNOS, ZNOT, ZNOU, ZVOR, ZVOQ, ZVOP
Please select the best answer from the choices provided

Answers

I think it’s A it looks like it so I think it is

Find the mean, median, mode, and range of the following data.

10, 20, 30, 15, 90, 80, 35, 30, 25, 15, 60, 75, 80, 30, 45, 35, 95, 80, 80, 25, 15

Answers

Mean (average) - add all numbers up and divided by the number of addends

Mean = 46.19047619 (50)

Median - arrange numbers in numerical order, and find the one in the middle

Median = 35

Mode - number that appears the mode

Mode = 80

Range - difference between biggest and smallest number

Range = 80

~theLocoCoco

how to graph y = x^2+3

Answers

Answer:

regular parabola but shifted up 3 on the y axis

Step-by-step explanation:

Complete the product of: 0.25 x 2 =
A. 0.75
B. 0.50
C. 1.50
D. 0.20
С C

Answers

Answer:

B is the answer for the question

The answer is B. 0.50

For what value of k will the lines x+2y=0, 3x-4y-10=0 and 5x+ky-7=0 are concurrent?​

Answers

Answer:

After solve the equations we get value of k=3

Step-by-step explanation:

We need to find value of k for which the lines x+2y=0, 3x-4y-10=0 and 5x+ky-7=0 are concurrent.

If the lines are concurrent, they pass through same point.

Let:

[tex]x+2y=0--eq(1)\\ 3x-4y-10=0--eq(2)\\ 5x+ky-7=0--eq(3)[/tex]

First solving equation 1 and 2 to find values of x and y

From eq(1) we find value of x and put it in eq(2)

[tex]From \ eq(1) x+2y=0\\x=-2y\\Put x=-2y \ in \ eq(2)\\3x-4y-10=0\\3(-2y)-4y-10=0 \\-6y-4y=10\\-10y=10\\y=\frac{10}{-10}\\y=-1[/tex]

After solving we get value of y=-1

Now putting in eq(1) to get value of x

[tex]x+2y=0\\x+2(-1)=0\\x-2=0\\x=2[/tex]

So, Value of x= 2

Now put value of x=2 and y=-1 into eq(3) to find value of k

[tex]5x+ky-7=0\\5(2)+k(-1)-7=0\\10-k-7=0\\-k+3=0\\-k=-3\\k=3[/tex]

So, After solve the equations we get value of k=3

100 points to the people who answer and you'll be reported if answer with something stupid
Y'all, what's another way to say "dramatic flare"
please and thank you:)

Answers

Answer:

another way to say dramatic flare is flamboyant which means to be loud and dramatic like saying the shirt with the parrots on it is very flamboyant

Step-by-step explanation: brainliest plz

The sum of three consecutive numbers is 84. What is the largest of these numbers? (1 point)

26
27
28
29

WILL GIVE BRAINLEST!!!!!!

Answers

Answer:

29

Step-by-step explanation:

First, we have to find three numbers out of the four that add up to 84. But, it has to be in order because the question says consecutive numbers. In case you don’t know, consecutive numbers are numbers that increase at the same rate. In this problem, the numbers increase by one. I first did 26+27+28, which equaled 81. I have to get to 84 though. So, I did 27+28+29, which equaled 84. I did it correctly because 27, 28, and 29 are consecutive number, since they go inorder, and I added them up to 84. But the question is asking which of the three is the largest number. So, out of 27, 28, and 29, 29 is the largest number.

Hope this helps and answers your question! :)

Answer:

Step-by-step explanation:

i just took the test its 29

Find the value of 2x+y when x=4 and y3

Answers

Answer:

11

Step-by-step explanation:

Replace the values of x and y into the equation.

2(4) + 3 = 8 + 3

            = 11

Here’s your answer it’s gonna be 11!!

Shauna made 8 of 13 free throws. What percent of her free throws did she make?

Answers

Search it up on google

It cost $15 to buy 6 pairs of socks.

Answers

thank you, I’ll be using this when I need 6 pairs of socks

IS THIS CORRECT OR NAH

Answers

Answer:

yes

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

Can someone please help me with this question I don’t understand it

Answers

Brand A: 32 Diapers, $8.99: about 28 cents per diaper

Brand B: 50 Diapers, $12.49: about 24 cents per diaper

You divide the amount of diapers by the money.

For example, 32 diapers/$8.99 equals about 28 cents per diaper and 50 diapers/$12.49 equals about 24 cents per diaper.

Brand B is the better deal since you save about 4 cents more.

2+2/4+7-9x(-5).

Please help me

Answers

Answer:

109/2 is the answer of your question . Use PEMDAS rule

Write a cubic function whose graph is shown

Answers

Answer:

f(x) = x³ - 2x² - x + 2

Step-by-step explanation:

Since, the graph attached has three zeros (x-intercepts) at x = -1, 1 and 2,

Equation of the given function will be,

f(x) = (x + 1)(x - 1)(x - 2)

By solving this equation,

f(x) = (x² - 1)(x - 2)

     = x²(x - 2) - 1(x - 2)

     = x³ - 2x² - x + 2

Therefore, answer  will be f(x) = x³ - 2x² - x + 2.

The cubic function will be "f(x) = x³ - 2x² - x + 2".

According to the given graph,

Three zeros,

x = -1, 1, and 2

The function will be:

→ [tex]f(x) = (x+1)(x-1)(x-2)[/tex]

By solving this, we get

          [tex]= (x^2-1)(x-2)[/tex]

          [tex]= x^2(x-2)-1(x-2)[/tex]

          [tex]= x^3-2x^2-x+2[/tex]

Thus the function above is right.

Learn more about cubic function here:

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ok yall i need help and yall kinda no treading the question fully READ ITTTTT, i will give brainleist

Answers

Answer:have a wonderful Christmas!

Step-by-step explanation:70+95

70=2*5*7

95=5*19

70+95=(5*2*7)+(5*19)=(5*14)+(5*19)=5*(14+19)=5*(33)

5*33=165 and 70+95=165 also

Answer:

The answer is 165, hope this helps.

Step-by-step explanation:

Find the prime factors of each term in order to find the greatest common factor (GCF).

Find the x-intercept of the following linear function: 3x - 2y- 16
QUICK

Answers

I gotchu

To solve for x-intercepts, y must be 0.

3x - 2(0) - 16 = 0

3x - 16 = 0

3x = 16

x = 16/3

X intercepts are ([tex]\frac{16}{3}[/tex],0)

Answer:

The answer is 5.33333333 or 5 1/3

Find the slope of UV.*
Ау
S(1, 4)
4
T(5, 3)
V-1, 2)
U(3, 1)
-2.
N.
4
6 x

Answers

Answer:

The slope of UV = 4

Step-by-step explanation:

Given the points

U(3, 1)V(-1, 2)

Finding the slope of UV

[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\left(x_1,\:y_1\right)=\left(-1,\:1\right),\:\left(x_2,\:y_2\right)=\left(-2,\:-3\right)[/tex]

[tex]m=\frac{-3-1}{-2-\left(-1\right)}[/tex]

[tex]m=4[/tex]

Thus, the slope of UV = 4

VX
Mr. Chang's class has 28 students, 7 of whom are girls. Which equation shows how to determine the number of girls
in Mr. Chang's class?

Answers

28 *4/7 = 16 in Mr Chang’s class

Help please !!! ASAP

Answers

3 goes 1, 4 goes 2, 1 goes 3 and 2 goes last

3. If Ted is making monthly payments of $77 on a loan of $4,000 for 5 years;
approximately what percent interest is he paying?
$

Answers

answer: about 1.93%
hope this helps

The percent of interest is he paying is,

⇒ R = 4.62%

What is mean by Percentage?

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

To Calculate the percent of a number , divide the number by whole number and multiply by 100.

We have to given that;

Ted is making monthly payments of $77 on a loan of $4,000 for 5 years.

Hence, Yearly payments to pay is,

⇒ 12 × 77

⇒ $924

Hence, We get;

⇒ Interest = PRT/ 100

⇒ 924 = 4000 × R × 5 / 100

⇒ 92400 / 20,000 = R

⇒ R = 4.62%

Thus, The percent of interest is he paying is,

⇒ R = 4.62%

Learn more about the percent visit:

https://brainly.com/question/24877689

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If Aaron tunes into his favorite radio station at a randomly selected time, there is a 0.20 probability that a commercial will be playing.
Interpret this probability as a long-run relative frequency.

Answers

Answer:

This simply means that, on a scale of 1 - 100, there is a 20 percent chances that, when Aaron tunes into the radio frequencies in search of a station, he will be able to get one station playing a commercial at that particular time.

For example, at 11:00am each day, him tuning into his favorite radio station would be 20 percent possible to meet one playing a commercial.

Step-by-step explanation:

Using the concept of relative frequency, the interpretation is that over a large number of days, in around 20% of the times he tunes is his favorite station a commercial will be playing.

A probability of an outcome A of a% means that over a large number of experiments, the relative frequency(which is the number of desired outcomes divided by the number of total outcomes) of event A will be of [tex]\frac{a}{100}[/tex].

In this problem, there is a 0.2 probability of a commercial playing when he tunes in his favorite station.Hence, the interpretation is that over a large number of days, in around 20% of the times he tunes is his favorite station a commercial will be playing.

A similar problem is given at https://brainly.com/question/16967884

check if 7 is a solution of the equation 4 ( Z - 3 ) = 16. step by step plz guys. ​

Answers

Answer:

YES

Step-by-step explanation:

4(Z-3)=16

4Z-12=16

  +12 +12

4Z=28

Z=7

Answer:7

Step-by-step explanation:

4(z-3)=16

4z-12=16

4z=28

4z/4=28/4

z =7

What is the value of the missing exponent in the equation 7.4 ÷ 10= 0.074?

Answers

the answer is 0.74 not 0.074

Step-by-step explanation:

7.4 ÷ 10 = 0.74

PLEASE HELP URGENT I NEED THIS LIKE RIGHT NOW PLEASE HELP MEEEEEEEE

Answers

Answer:

45

Step-by-step explanation:

Answer:

The length of the body is 45.

Step-by-step explanation:

The violin and bass have an equal ratio, to find the ratio find the two given lengths and divide them, 72 ÷ 24 = 3. So the ratio is 3:1. To find the body of the bass you just have to do 15 × 3. Which is 45.

A booth at the farmer’s market has fresh goat cheese in three sizes of containers. The big container is 30 ounces and costs $9.00. The medium container is 15 ounces and costs $4.95. The small container is 8 ounces and costs $2.00. What size is the best buy? Justify your reasoning.

Answers

Answer:

8 ounce

Step-by-step explanation:

The 30 ounce container costs $0.30 per ounce. The 15 ounce container is $0.33 per ounce. The 8 ounce container is $0.25 per ounce. Therefore, the 8 ounce container costs less per each ounce.

f(t) = 2t - 3 f(7) =

Answers

Answer:

f(7) = 11

Step-by-step explanation:

t = 7, so we can just plug in the value 7 for (t) in the given equation.

f(t) = 2t - 3

  f(7) = (2 × 7) - 3

  f(7) = 14 - 3

  f(7) = 11

please help me
a piece of wire is 28cm in length is cut into two parts, each part bend to make a square. given that area of square is 416m^2. find the perimeter of each square.

Answers

Answer:

25.488 cm and 2.512 cm

Step-by-step explanation:

Note: the area of squares is 41 cm² but not 416 m², typo

Let the sides of squares be x and y

Based on given we have equations:

4x + 4y = 28x² + y² = 41

Simplify the first equation

4x + 4y = 28x + y = 7x = 7 - y

Substitute x to solve for y:

(7 - y)² + y² = 4149 - 14y + y² + y² = 412y² - 14y + 49 - 41 = 02y² - 14y + 8 = 0y² -7y + 4 =0

Solving we get:

y= 6.372 cm or y= 0.628cm

Then

x = 0.628 cm or x = 6.372 cm

Perimeter of each square is:

4*6.372 = 25.488 cm

and

4*0.628 = 2.512 cm

can someone please help me with this question??

Answers

Answer:

2nd one

Step-by-step explanation:

$100 is borrowed at 9% interest per year. How much is owed after one year if interest is compounded :
a. annually?
b. monthly?
c. continuously?

Answers

Answer:

Step-by-step explanation:

a). Formula to be used,

   A = P(1 + i)ⁿ

       = 100(1 + 0.09)¹

       = $109

b). Formula to be used,

   A = [tex]P(1+\frac{i}{12})^{12n}[/tex]

       = [tex]100(1+\frac{0.09}{12})^{12\times 1}[/tex]

       = [tex]100(1+0.0075)^{12}[/tex]

       = 100 × 1.0938

       = $109.38

(c). Formula to be used,

     A = [tex]Pe^{i\times n}[/tex]

         = [tex]100e^{1\times 0.09}[/tex]

         = [tex]100(e)^{0.09}[/tex]

         = $109.42

The graph below shows where the two functions y = f(x) and y = g(x) intersect. Solve the equation f(x) = g(x).

Answers

Answer: (-2, 2) and (4, 8)

There are two solutions because the two functions cross each other twice.

The solutions of the equation f(x) = g(x) are (4, 8) and (-2, 2).

We have a graphical representation of two functions f(x) and g(x) and where they intersect.

We have to solve the equation f(x) = g(x)

Two functions A(x) and B(x) are plotted on the graph such that these these two functions intersect each other at three different coordinates. The total number of solutions possible for - A(x) = B(x) is ?

The total number of solutions can be calculated by counting the points at which these curves intersect each other. Hence, the total number of possible solutions are 3.

In the question given - We have a straight line and a parabola -

Now, we just have to look at the points at which these two graphs intersect each other. It can be seen that - both the graphs cut each other at coordinates - (4, 8) and (-2, 2).

Hence, the solutions of the equation f(x) = g(x) are (4, 8) and (-2, 2).

Alternative Method -

The general equation of straight line is : y = mx + c and that of parabola is : y = [tex]\sqrt{4ax}[/tex]

The solution can be calculated by equating both of the above expressions and solving them.

mx + c = [tex]\sqrt{4ax}[/tex]

To solve more questions on solving the equations, visit the link below -

https://brainly.com/question/1386163

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