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

Convert 51.7% to a fraction in simplest form and a decimal.

Answers

0.517 as a decimal 517/10 as a fraction

uses 2 1/2 cups of apple juice and 1 1/2 of carrot juice for a recipe. enter the number of cups of apple juice used for 1 cup of carrot juice

Answers

Answer:

1 3/4

Step-by-step explanation:

Please help! I will give brainliest!!!!!!

Answers

Answer:

3,10 please give me brainliest i need one more for 5 please please  please

Step-by-step explanation:

Find the volume and surface area of each prism 3cm by 3cm by 3cm

Answers

Answer:

3 x 3 x 3= 18  so 18cm squared

Step-by-step explanation

Answer:

Volume =27cm³

Total surface area=54cm²

Step-by-step explanation:

Formula for finding volume of an object is Volume =length×breadth×height

so V=3cm×3cm×3cm=9cm²×3cm=27cm³ because the cm is three so it will become cube.

Formula for finding the total subject of an object is T.S.A meaning total surface area=2((length ×breadth)+(length×height)+(breadth ×height))

so it will be 2((3cm ×3cm)+(3cm ×3cm)+(3cm ×3cm)) calculate and if you any problem let me know.

Doe has 2 3/8 pounds of hamburger meat. He is making 1/4 pound hamburgers .Does doe have enough meat to make 10 hamburgers

Answers

He doesn’t have enough, he has 19/8 and needs 20/8 for 10 burgers, he’s missing 1/8 :)


What is the slope of a line parallel to the line whose equation is 2x+y=6.

Answers

Answer:

-2 is the slope...

So Basically -2/1

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

First, you solve for y by subtracting 2x from both sides of the equation and so now we have a y= -2x+6. The slope is going to be the number that is with x.

A computer manufacturer has found that its expenditure rate per day (in hundreds of dollars) on a certain type of job is given by where x is the number of days since the start of the job. Find the expenditure if the job takes 8 days.

Answers

Answer:

The expenditure would be $ 8600

Step-by-step explanation:

If the cost is given by the function

C(x)= 10x + 6   where x is the number of days

The cost for 1 day would be

C(1)= 16 *100 = 1600 $  ( the expenses are in hundreds of dollars)

Then Putting x= 8 in the given equation we get

C(8)= 10(8) + 6  

= 86

Multiplying 86 by 100 because expenditure rate per day  is in hundreds of dollars

The expenditure would be $ 8600

In the figure, BE||CD, B is the midpoint of AC, and E is the midpoint of AD

Answers

Answer:

A. 8

Step-by-step explanation:

BE = ½(CD) (midsegment theorem)

BE = 2x - 10

CD = 12

Plug in the values

2x - 10 = ½(12)

2x - 10 = 6

Add 10 to both sides

2x - 10 + 10 = 6 + 10 (addition property of equality)

2x = 16 (addition property of equality)

Divide both sides by 2

2x/2 = 16/2

x = 8 (division property of equality)

find the distance from point A to the given line
A(2,-1), y=-x+4

Answers

Answer:

using distance formula you can solve it

what is the equation for (4, 9.4) and (-3, -9.5)

Answers

Answer: I got an eqaution I hope it is basic

Step-by-step explanation:

4 times 9

9 - (-3 ) times -9 + 5

How do solve this problem?
find an equation of a line parallel to the given line and contains the given point. Write the equation in slope–intercept form. line 2x + 5y= -10 point (10, 4)

Answers

Answer:

y=-2/5x+8

Step-by-step explanation:

Step 1: Begin by changing the equation into slope-intercept form. Subtract 2x to both sides to get 5y=-10-2x. Divide 5 to both sides to isolate the variable, y. You should get y=-2/5x-2.

Step 2: Because we are looking for a line parallel to the given line, the slope should be the same, but the y-intercept should be different. Remove -2 to replace it with b, so it's unknown. The equation should be y=-2/5x+b. Plug in the ordered pair, (10, 4), into the equation to get 4=-2/5(10)+b. Multiply -2/5 and 10 to get -4. Add -4 to both sides and b=8. Plug in 8 and your final equation should be y=-2/5x+8.

URGENT DUE AT 1:00 PLZ HELP... MATH123456

Answers

Answer:

Step-by-step explanation:

Nose

Theresa finds a shirt on sale at the store. The regular price of the shirt is $32.00. But there is a 20% off sale today. Theresa remembered that there is 8.1% tax on the sale price of the shirt. What is her final cost?

Question 10 options:

$28.92


$27.67


$29.31


$31.00

Answers

Answer:

Step-by-step explanation:

Given tgat:

Regular price = $32

Discount = 20%

Sale tax = 8.1%

A car travels around a circular track of radius 1.5 miles. It traversed35of a complete revolution. Howfar did it travel?

Answers

Answer:

The total distance traveled by the car is 330 miles.

Step-by-step explanation:

The circular track is the circumference of circle with radius 1.5 miles.

Circumference of a circle = 2[tex]\pi[/tex]r

Thus,

Circumference of the track  = 2 x [tex]\frac{22}{7}[/tex] x 1.5

                           = 9.4286571429

Circumference of the track = 9.4286571429 miles

But, one complete revolution by the car is the circumference of the track.

i.e One complete revolution round the track = 9.4286571429 miles

Therefore,

35 complete revolutions round the track = 35 x 9.4286571429 miles

                                       = 330 miles

The total distance traveled by the car is 330 miles.

at a pet store at the mall there are 21 dogs, 13 cats, 12 rabbits, 5 hamsters, and 3 ferrets. What percent of the animals mare rabbits

Answers

Answer:

28.57%

Step-by-step explanation

I added all the animals together and got the precentage of rabbits

Hopefully its right :)

Please help me out quickly

Answers

Answer:

I dont see the stuff I think my internet is slow but I will help you when its up again im using hotspot just remind me

Step-by-step explanation:

What is the point-slope form of the equation of the line that passes through the point (-3,-4) and has a slope
of 2?

Answers

Answer:

y=2x+6

Step-by-step explanation:

Answer:

y=2x+2

Step-by-step explanation:

To find the point-slope form of the equation we need to get the slope-intercept form of (-3,-4) and 2

(Slope intercept form formula is y=mx+b) (m is slope) (b is y-intercept)

So we know that the slope of this equation is 2 so we can replace m with 2 since the slope is 2 and m is slope.

Equation will look like this:

y=2x+b

Now we need to find the b or y-intercept of the equation to do this the (-3,-4) come into play: replace x with -3 and replace y with -4

(x,y) -3 is x since it is the same spot in (-3,-4) and -4 is y since it is in the same spot in (-3,-4)

Replace:

-4=2(-3)+b

Multiply 2 and -3:

-4=-6+b

Move 6 to the other side by adding 6 on both side:

6-4=-6+6+b

Simplify

2=b

Now the equation looks like this: (If you replace b with 2 in y=2x+b)

y=2x+2

Answer: y=2x+2 (Point-slope form is the same thing as slope-intercept form)

Mrs. 1 ran 10 meters in 3.8 seconds. Mrs. 2 ran 10 meters in 3.2 seconds.
Who ran faster?

Answers

Answer:

Mrs. 2

Step-by-step explanation:

3.2 seconds is shorter than 3.8 seconds

Answer:

Mrs 2 ran 10 meters in 3.2seconds

HELP QUICK!! what is the effect on the graph of the function y=x^2 when it is changed to y=1/2x^2?

a) the graph moves up the y axis b) the graph moves down the y axis c) the graph narrows d) the graph widens

Answers

Answer:

D is your answer

hopefully this helps

The vertices of a triangle are P(-2, -4), Q(2, -5), and R(-1,-8). Name the vértices of the triangle after reflecting over the x-axis

Answers

Answer:

P(-2,4)

Q(2,5)

R(-1,8)

Step-by-step explanation:

The rule for reflecting points across the x-axis is to keep the x-value the same but "negate" the y-value. So, the points above are your answers.

b. Determine if x ^ 2 - 9x + 14 is always positive, always negative , or neither for all negative values

Answers

negitive is the answer i think

look at picture and answer ASAP

Answers

Answer:

its B and A

Step-by-step explanation:

Answer:

its in between the fist and second one cuusing what is given thats what i figured out

Step-by-step explanation:

3 x 36= 108 / 3 x 15 = 45

9 x 12 = 108 / 9 x 5 = 45

6 x 18 = 108 / 6 x 7 = 42

i hope this helps :)

log(5t)(5t + 1) * log(5x+1) (5t + 2) * log(5t+2 )(5t + 3)... log(5t+n)(5t +n +1)​

Answers

I assume you're referring to the product,

[tex]\log_{5t}(5t+1)\cdot\log_{5t+1}(5t+2)\cdot\cdots\cdot\log_{5t+n}(5t+n+1)[/tex]

Recall the change-of-base identity:

[tex]\log_ab=\dfrac{\log_cb}{\log_ca}[/tex]

where c > 0 and c ≠ 1. This means the product is equivalent to

[tex]\dfrac{\log(5t+1)}{\log(5t)}\cdot\dfrac{\log(5t+2)}{\log(5t+1)}\cdot\cdots\cdot\dfrac{\log(5t+n+1)}{\log(5t+n)}[/tex]

and it telescopes in the sense that the numerator and denominator of any two consecutive terms cancel with one another. The above then simplifies to

[tex]\dfrac{\log(5t+n+1)}{\log(5t)}=\boxed{\log_{5t}(5t+n+1)}[/tex]

Antonio purchased adult and child tickets for the fair. Tickets cost $29.35 for each adult and $17.45 for each child. Let x represent the number of adult tickets purchased and y represent the number of child tickets purchased. Write an expression to represent the total cost of the tickets Antonio purchased

Answers

Answer: B

Step-by-step explanation:

It is $29.35 for each of the tickets that they buy for adults, so to figure out how much it is for all the adult tickets, it would be $29.35 times x. Same for the children tickets except it is times y and the amount of money is different.

A factory employs over 3000 workers, of whom 30% are women. If the 15 members of the union executive committee were chosen from among the workers without regard to gender

Answers

Answer:

I think 4000 worker and I will be there at some point today and I

1. Given: y = -2x2
Domain
Range
Opening of the
parabola
Vertex
Axis of Symmetry
X - intercept
y - intercept​

Answers

Domain: (-∞,∞) or -∞ < x < ∞ or all real numbers

Range: (-∞,0] or -∞ < y ≤ 0

Opens: Downwards since a is negative

Vertex: ( 0 , 0 )

Axis of Symmetry: x=0

x-intercept: ( 0 , 0 )

y-intercept: ( 0 , 0 )

Can you help me with this question please by the way its not 101

Answers

Answer:

41

Step-by-step explanation:

101+38=139

180-139 = 41

Calculate the paychecks of the following people. Select the total hours and paycheck.

Answers

Answer:

If the numbers under the days of the week are the hours worked then the answers are Sue-40,$6.75,$270 Jerry-30,$5.15,154.5  Sam-38.75,$8.75,339 Step-by-step explanation:

Just add up the number of hours worked and multiply by the rate.

Find the equation of the line that passes through (4,4) and is parallel to y = 2x + 4.
Leave your answer in the form y= mx + c

Answers

Answer:

x,y(0,12)

Step-by-step explanation:

Y=mx+c

4=2X+4

4=2x+4

2x=0

X=0

Y=mx+c

Y=2(4)+4

Y=8+4

Y=12

What is
0.74314482
as a fraction?

(I don’t have my TI Calculator with me and that is what I need to figure out this question)

Answers

The answer is

3715731 over 5000000
Other Questions
Arrange the integers 1,4,8,12,17,32 so that all consecutive integers add to a perfect square. Enter your answer with numbers separated by commas. During the time of the Boston Tea Party many women in the colonies boycotted English sugar for their tea. True False Josh plans to spend at most $45 on a gift for his mother, including the $15 he plans to spend on flowers. Which inequality represents x, the range of amounts that Josh can spend on the gift? 8 - 5.5 =10.5 - 8=13 - 10.5 =15.5 - 13= Question 2 of 10Aubrey didn't like to use graphics or images on her slides. She preferred touse only a title for her slides and bullet-pointed text: What is the best thingyou could say to Aubrey about using media that might change her mind?O A. As long as you use it responsibly, it will only enhance your slidesand engage your audience.B. Media will keep your audience entertained and take the pressureoff of the presenter.C. You should always tryslide.include as much media as you can on aD. Actually, Aubrey's beliefs are well founded and backed up byresearch 29. Is the listed activity aerobic or anaerobic? Roller SkatingAerobicAnaerobic Why did Napoleon send troops to Saint-Domingue? What happened to them?Authorized only to negotiate for the purchase of New Orleans or access to theMississippi River, they instead negotiated the purchase of the entire 827,000square miles of Louisiana.He sent troops to reclaim the colony and reestablish slavery and the sugar trade.Disease killed most of them.They felt that Napoleon had abrogated his treaty obligations but could not doanything about it. Bacon's purpose is to explain whatO Chaos is.O Love is.O Night is.O Venus is. native Americans crossed the continents as nomadic hunters after mammoths,giant bison, and ___ A. Lions B. Mastodons C. Alligators D. Bears How can I use a model to solve 1.4 divided by 4? Rewrite with only sin x and cos x.cos 2x + sin x 1 + 3 sin x 1 + 3 sin2x 1 - 2 sin2x + sin x 1 + 2 sin2x + sin x can i get some help What type of art would you do if presented with the task of creating art ina public space? Explain what you would create and where you woulddisplay it. give me your ideas! What is the least common denominator of 7/12, 7/15, and 7/24? Each time a certain ball hits the ground, it bounces up 2/3 of its previous height. If the ball is dropped from 27 inches off the ground, what will be the height of the ball after the third bounce? * Need help answer this question please help me Find the value of x.A. 20B. 17C. 22D. 15 This was due 12 minutes ago but whatever 10 points! Daryl has a scholarship that pays 80% of his tuition for all four years he attends college. What is the total value of the scholarship if the tuition is $13,500 per year? Within a major, students can choose to study a specific area within thatmajor. For example, a journalism student may study military journalism orbusiness journalism. This specific area is called aA. liberal studyB. minorC. specializationO D. broad requirement