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

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.

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]

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.

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

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)

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.

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

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:

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 :)

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.

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 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

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 :)

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

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.


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.

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

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.

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 )

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

Answers

0.517 as a decimal 517/10 as a fraction

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)

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

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 :)

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%

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

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:

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:

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

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

Answers

Answer:

Step-by-step explanation:

Nose

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