Standing on the edge of a​ cliff, Fernando throws a rock upward from a height 512 feet above the water at a speed of 64 feet per second. How long will it take for the rock to land in the​ water?

Answers

Answer 1

Answer: 7.6875 seconds.

Step-by-step explanation:

Let's writhe the motion equations for the rock.

The only force acting on the rock will be the gravitational force, then the acceleration of the rock will be the gravitational acceleration g ≈ 32 ft/s^2

A(t) = -32ft/s^2

Where we have a negative sign because this acceleration pulls the rock downwards.

For the velocity, we must integrate over time, and the constant of integration will be equal to the initial velocity of the rock = 64 ft/s, then the velocity equation is:

V(t) = (-32ft/s^2)*t + 64m/s

For the position, we integrate again over time, and this time the constant of integration will be the initial position, 512ft (Then the water level is at 0 ft)

P(t) = (1/2)*(-32ft/s^2)*t^2 + 64m/s*t + 512 ft

Now we want to find the value of t, the time, such that the rock hits the water.

The rock will land in the water when P(t) = 0ft, becuse we defined the zero in the position as the water.

Then we must solve:

P(t) = 0ft = (1/2)*(-32ft/s^2)*t^2 + 64m/s*t + 512 ft

for t, let's solve this:

0ft = (-16ft/s^2)*t^2 + 64m/s*t + 512 ft

This is a quadratic equation. the two solutions can be found by using the Bhaskara equation, then the solutions will be:

[tex]t = \frac{ -64ft/s +- \sqrt{(64ft/s)^2 - 4*(-16ft/s^2)*512ft} }{2*(-16ft/s^2)} = \frac{-64ft/s +- 192ft/s}{-32ft/s}[/tex]

Then the two solutions are:

t = (-64ft/s + 192ft/s)/(-32ft/s^2) =  -4s      (This time is negative, which is no really defined for this problem, so we can discard this solution)

The other solution is:

t = (-64ft/s - 192ft/s)/(-32ft/s^2) = 7.6875 s

This solution makes sense with the problem, then the answer is 7.6875 seconds.


Related Questions

Plz help me with these 2 algreba problems

Answers

For number 2, all of the statements are correct. If f(x)=x and g(x)=f(2x), then g is twice the slope of f. Since both of them have a b value of 0, they both have the same y-intercept. When the b is 0 then the line crosses the origin.

For number 3 it’s A because when the equation is y=-3 it means that there’s a straight horizontal line going through the point (0,-3), thus the slope is 0. This equation can be looked at as y=0x-3 because the -3 is the b.

If the equation was x=-3 then there would be a straight vertical line going through the point (-3,0)

Hope this helps!

PLEASE HELP

write the equation and solve

Answers

Answer:

min 5 max 11

Step-by-step explanation:

aloud to go up or down 3

find min and max

8-3=5

8+3=5

SI EL PORCENTAJE DE INTERÉS ES DEL 18% ANUAL . Y EL CONVENIO DE PAGO ES BIMENSUAL, ENTONCES LAS VECES QUE SE PAGA EL INTERES ES :

a. DOS VECES EN EL AÑO
b. VEINTE Y CUATRO VECES EN EL AÑO
c. SEIS VECES EN EL AÑO

Answers

Answer:

C. Seis veces en el año.

Step-by-step explanation:

Un año consiste en 12 meses y seis períodos de dos meses (bimestres). Entonces, el convenio de pago establece claramente que se 18 por ciento de interés cada dos meses, lo cual significa que se paga seis veces al año por concepto de intereses.

Entonces, la respuesta correcta es C.

Need help!
Hey does anybody mind helping me with this question? It’s in the picture also tysm if u answer I will mark u Brainly back!!! Have a great day everyone

Answers

Answer:

8/11

Step-by-step explanation:

Answer:

2 2/3+3 2/3

2+3 + 2/3+2/3

5 + 4/3

5 + 1 1/3

6 1/3

The third one is your answer, also thank you. I hope you have a great day as well.

-2(x+4)=12
please explain what to do .​

Answers

Answer:

x = -10

Step-by-step explanation:

First I would expand by distributing the left side.

Using distribution the new equation would be: -2x - 8 = 12

Now, I would move constants to one side and keep variables on the other side.

Doing this, my new equation would be -2x = 20

Now I would divide both sides by negative 2, giving the answer x = -10

Answer: -10

Step-by-step explanation:

1/3 divided by 2/5 help me plss

Answers

Answer:

5/6

Step-by-step explanation:

dividing means you gotta flip it to multiplication.

1 times 5 = 5

3 times 2 = 6

Write an equation in slope-intercept form for a line that passes through the point (4,-8) and is parallel to the line y=-3x+7

Answers

Answer:

[tex]y=-3x+4[/tex]

Step-by-step explanation:

What is the value of y in the solution for this system of equations? 2x – 3y = 13 1 7. y = 5x - 2​

Answers

The value of y in the solution for this system of equations is -61/13.

What is Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

2x – 3y = 13 and y = 5x - 2​

Solving the Two Equation we get

2x - 3(5x -2) = 13

2x - 15x + 6 = 13

-13x = 13 -6

-13x = 7

x= -7/13

and, y= 5(-7/13)- 2

y = -35/13- 2

y = -61/13

Learn more about Equation here:

https://brainly.com/question/29657983

#SPJ1

Answer:

Its B on EDG 2023

Step-by-step explanation:

edg 2023

When I bought my car it was $25,000. My car’s value is now $11,000. What percentage is my car now from its original price?

Answers

Answer:

56% should be the answer

Naomi surveyed 480 of the students in her school about their favorite color. 95% said their favorite color was red. How many students favorite color was red?

Answers

Answer:

77

Step-by-step explanation:

88e3838383883

I need help anyone plz?

Answers

Answer:

Step-by-step explanation:

all of them are correct

shopkeeper did 13 x (value of 1 bagel- $1.25) which is 16.25

Jada did (value of 6 bagels- $6)x2+ (value of 1 bagel- $1.25) which is 13.25

Priya did (valuse of 9 bagels- $8)+ (value of 1 bagel - $1.25)x4 which is 13

Han did (value of 12 bagels- $10)+ (value of 1 bagel) which is 11.25

The blue dot is at what value on the number line? Pls help??

Answers

Answer:

4

Step-by-step explanation:

the question is on then sheet ​

Answers

Answer:

6[tex]m^{2}[/tex][tex]n^{2}[/tex]-4mn+6

Step-by-step explanation:

PLEASE MARK BRAINLIEST I ONLY NEED 1 MORE!!!!!!!!!

[tex] = (11 {m}^{2} {n}^{2} + 2mn - 11) - (5 {m}^{2} {n}^{2} - 6mn + 17)[/tex]

[tex] = 11 {m}^{2} {n}^{2} + 2mn - 11 - 5 {m}^{2} {n}^{2} + 6mn - 17[/tex]

[tex] = (11 {m}^{2} {n}^{2} - 5 {{m}^{2} } {n}^{2} ) + (2mn + 6mn) + ( - 11 - 17)[/tex]

[tex] = 6 {m}^{2} {n}^{2} + 8mn - 28[/tex]

The other person is wrong

I can say that for sure.

Percentage Questions

Answers

Answer:

At the end of three months, you will owe £767

Step-by-step explanation:

First you find 7% of 1000

= 70

70 is added to the £1000 every month so

1070 - 150 = 920

990 - 150 = 840

917 - 150 = 767

which function has a restricted domain

Answers

Answer:

Restricted Domain. The use of a domain for a function that is smaller than the function's domain of definition. Note: Restricted domains are commonly used to specify a one-to-one section of a function.

Step-by-step explanation:

GOT U bro

evaluate the function: F(x)=-3+7 when x=6
(20pts)I NEED ANSWERS ASAP PLEASEE

Answers

Answer:

f ( 6 ) = 11  

Explanation:We want to plug in  6  for wherever we see x in the original function.

f

(

6

)

=

3

(

6

)

7

f

(

6

)

=

18

7

f

(

6

)

=

11

Step-by-step explanation:

Find the
total price of the item.
football: $18.33
tax: 6%
What is the total price of the item if the original price is $18.33 with the tax of 6%

Answers

Answer:

the total price will be 19.43

Identify the equation that has the same slope as the points (-1, 11) and (2, -10) .

a. y = -4x - 3

b. y = 3x + 3

c. y = x + 1

d. y = -7x + 4

Answers

Answer: for.-7x+4

Step-by-step explanation:

Formula for slope: m=y2-y1/x2-x1

Plug it in: (-10-11)/(2--1) = -21/3 = -7

M= -7

Y=mx+b

Y=-7x+b

11=-7(-1)+b

11=7+b

-7 -7

Y=-7x+4

I hope you can understand the explanation.....

Lean runs five laps around a track in 6 miles how many minutes per lap is that

Answers

Answer:

1.2

Step-by-step explanation:

divide 6 by 5

Answer:

8/1 or 8 minutes per lap

Step-by-step explanation:


1. Dilate A using P as the center of dilation and a scale factor of 3. Label the new point
A'.
2. Dilate Busing Pas the center of dilation and a scale factor of 2. Label the new point B'

Answers

Answer:

Step-by-step explanation:

Rule for the dilation of a point by a scale factor 'k',

(x, y) → (kx, ky)

If we impose this rule in this problem,

k = [tex]\frac{\text{Distance of A' from P}}{\text{Distance of A from P}}[/tex]

1). If k = 3

   Therefore, Distance of A' from P = 3(Distance of A from P)

   And point A' will be on the third circle.

2). If k = 2

   Distance of B' from P = 2(Distance of B from P)

   Since, B is on circle 2, B' will be on circle 4.

Now we can plot these points A' and B' on the graph.

After the dilation point A becomes A' and it is at a distance of 3 units from point P and after the dilation point B becomes B' and it is at a distance of 2 units from point P.

1)

Given :

Dilate A using P as the center of dilation and a scale factor of 3.

Let the coordinates of point A be (x,y) then after dilation point A becomes A'(3x , 3y). So, the distance of the point A' from the point P is 3 units

2)

Given :

Dilate Busing P as the center of dilation and a scale factor of 2.

Let the coordinates of point B be (x',y') then after dilation point B becomes B'(2x' , 2y'). So, the distance of the point B' from the point P is 2 units

For more information, refer to the link given below:

https://brainly.com/question/2856466

help meeeeeee!!!!!!!!!!!!!!!!!!!!!

Answers

Read this I have you some hint that should help you a bit don’t mode the writing lol

help me with this problem please ​

Answers

i think its all of the above ?? sorry if its wrong

HELP A MEEEE whats 1Million x 1Million

Answers

Answer:

one trillion

Step-by-step explanation:

What is 31.5% as a fraction (please help me with this one)

Answers

Answer:

63/2

Step-by-step explanation:

Answer:

63/200

Step-by-step explanation:

What is the answer ‍⬛


-1 1/5 + (-3/5)

Answers

Answer:

-9/5

Step-by-step explanation:

I am pretty sure this is it and hope it helps

helpp me plzzzzzzzzzzz i need it right noww

Answers

Answer:

1.B

2.D

3.A

4.E

5.C

Step-by-step explanation:

find the area of a circle with a radius of two either enter an exact answer in terms of pi or use 3.14 for pi and enter your answer as a decimal .​

Answers

Answer:

Step-by-step explanation:

Hope this helps. Pls give brainliest.

Answer:

I believe it would be 2 x 3.14= 6.28

( I said 2 because, isn't that the radius of the circle)

Step-by-step explanation:

Need help ASAP!!!!!!!

Answers

1. (X+2)
2. X+2
4. X = -2 √6 and x= 2 √6

). On a map the distance from Jan's house to school meaures 1.5 in. If the scale
that the map used was 1 in = 2 miles, what is the actual distance to Jan's school?

Answers

Answer:

2 miles and 0.5 in.

Step-by-step explanation:

if 1 inch eqauls 2 miles than think about it the 2 miles is for the 1 in 1,5 so it would be 2 miles and then you would have the 5 left so it woudl be 0.5 inches left.

The pair figures are similar.find the missing side

Answers

Answer:

C. x=3

Step-by-step explanation:

Because the sides are proportionate to each other

Side 3 is 3x the length of Side 1

Therefore,

Side 9 is also 3x the length of side X

3x=9

Divide both by 3

and X will be 3.

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