A rock is tossed vertically from a height of 2m with an initial velocity of 20 ms-1. The height of the rock, h, after t seconds can be modeled by the polynomial function :h(t)=−4.9t2+20t+2, t≥0. Calculate how many seconds, rounded to three significant figures, it takes for the rock to hit the ground.

Answers

Answer 1

Answer:

The rock takes 4.18 seconds to hit the ground

Step-by-step explanation:

Function Model

The height of a rock h, after t seconds, can be modeled by the polynomial function:

[tex]h(t)=-4.9t^2+20t+2, t\geq 0[/tex]

When the rock hits the ground, the height is 0, thus we need to find the value of t such as:

[tex]-4.9t^2+20t+2=0[/tex]

A quadratic equation can be expressed as:

[tex]at^2+bt+c=0[/tex]

where a,b, and c are constants.

Solving with the quadratic formula:

[tex]\displaystyle t=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

The values for the given equation are:

a=-4.9, b=20, c=2

Applying the formula:

[tex]\displaystyle t=\frac{-20\pm \sqrt{20^2-4(-4.9)(2)}}{2(-4.9)}[/tex]

[tex]\displaystyle t=\frac{-20\pm \sqrt{400+39.2}}{-9.8}[/tex]

[tex]\displaystyle t=\frac{-20\pm 20.957}{-9.8}[/tex]

There are two possible solutions:

[tex]\displaystyle t=\frac{-20- 20.957}{-9.8}=4.18[/tex]

[tex]\displaystyle t=\frac{-20+ 20.957}{-9.8}=-0.1[/tex]

Since t > 0, the only solution is t=4.19 seconds

The rock takes 4.18 seconds to hit the ground


Related Questions

can you guys please help​

Answers

Answer:

I cant read all of that. Im sure others ant either.

Step-by-step explanation:

Answer:

i cant read it for some reason, can you type it?

Step-by-step explanation:

{(5²)} ³×5⁴}÷5⁷ simplify and express the following as exponent​

Answers

Answer:

The answer is 5³.

Step-by-step explanation:

You have to apply Indices Law :

[tex] {a}^{m} \times {a}^{n} ⇒ {a}^{m + n} [/tex]

[tex] {a}^{m} \div {a}^{n}⇒ {a}^{m - n} [/tex]

[tex] { ({a}^{m} )}^{n} = {a}^{mn} [/tex]

So for this question :

[tex]( {( {5}^{2}) }^{3} \times {5}^{4} ) \div {5}^{7} [/tex]

[tex] = ( {5}^{6} \times {5}^{4} ) \div {5}^{7} [/tex]

[tex] = {5}^{10} \div {5}^{7} [/tex]

[tex] = {5}^{3} [/tex]


Lily drew 37 hearts and 36 circles. What is the ratio of hearts to circles?
Simplify your answer if possible.

Answers

Answer:

37: 36

Step-by-step explanation:

You can not simplify. Have a good day!

Which of the following sets represents a function?
O [(1, 2), (3, 2), (5, 7))
O [(3,5),(-1,7), (3,9)}
O [(1, 2), (1,4), (1, 6)

Answers

Answer:

(1, 2), (1,4), (1, 6)

Step-by-step explanation:

They're adding the Y-axis

Help Me pleasee i dont understand

Answers

To find slope on the graph you use rise/run like #1 you go up 3 and across 2 so it’s 3/2 and positive because the line is going up if it were going going down it’s a negative slope…now to find it with the formula it says it right there y2-y1 over x2-x1 for example 14-10 over -7-8 and simplify if you can…on the table you will do the same as you did with the formula on #15 you will use the formula like this 2-5 over -2+3 because we all know when you subtract a negative with a negative you’re basically adding them together

Which best represents the change in the vertices of rectangle ABCD to form rectangle A'B'C'D'?
F) (x, y ) → (2x, 2y)
G) (x, y ) → (1.5x, 1.5y)
H) (x, y ) → (3x, 3y)
J) (x, y ) → (4x, 4y)

Answers

Answer:

F

Step-by-step explanation:

On a coordinate plane, a line is drawn between points (negative 4, negative 3) and (negative 1, 4).

Use the Pythagorean theorem to find the distance on the coordinate plane.


a2 + b2 = c2


What is the distance between the two points?

StartRoot 20 EndRoot

StartRoot 40 EndRoot

StartRoot 45 EndRoot

StartRoot 58 EndRoot

Answers

Answer:

StartRoot 58 EndRoot

Step-by-step explanation:

Given the coordinates (-4, -3) and (-1, 4)

To get the distance between the two points, we will use the formula:

D =√(y2-y1)²+(x2-x1)²

From the coordinates, x1 = -4, y1 = -3, x2 = -1 and y2 = 4

Substitute

D =√(4-(-3))²+(-1-(-4))²

D = √(4+3)²+(-1+4)²

D = √7²+3²

D = √49+9

D = √58

Hence the correct option is D

StartRoot 58 EndRoot

Answer:

D. 58

Step-by-step explanation:

Write the word sentence as an equation. Then solve.
The difference between a number pand 6 is -14
Equation
Solution p=
25

Answers

Answer:

p - 6 = -14

p = -8

Step-by-step explanation:

       The difference between a number p and 6 is -14

  Let the number  = p;

Equation:

          difference between the numbers:

                         p - 6

          equality;

                         p - 6 = -14

Equation; p - 6 = -14

Solution:

                p - 6 = -14

            add (+6) to both sides of the expression;

                 p - 6 + (+6) = -14 +(+6)

                 p = -8

A quarterback dropped back 5 yards behind the lone of scrimmage. Then, he passed the ball 14 yards. How far past the line of scrimmage did the ball travel? (Write an equation to represent this problem)

Answers

Answer:

9 yards

Step-by-step explanation:

-5 + 14 = 9

Help me please.

Write a ratio expressing the slope of the line passing through (5,7) and (-3,-2).

Answers

Answer:

9/8

Step-by-step explanation:

change in y/change in x= slope

so in this case -9/-8 or 9/8 bc the negatives cancel out

Two uniformly charged, infinite, nonconducting planes are parallel to a yz plane and positioned at x " #50 cm and x " )50 cm. The charge densities on the planes are #50nC/m2 and )25 nC/m2 , respectively. What is the magnitude of the potential difference between the origin and the point on the x axis at x " )80 cm? (Hint: Use Gauss’ law.)

Answers

Two uniformly charged, infinite, nonconducting planes are parallel to a yz plane and positioned at x = -50 cm and x = +50 cm. The charge densities on the planes are -50 nC/m² and +25 nC/m², respectively. What is the magnitude of the potential difference between the origin and the point on the x axis at x = +80 cm? (Hint:Use Gauss’ law.)

Answer:

ΔV = 2520 V

Step-by-step explanation:

We are given;

Charge density 1; σ1 = -50 nC/m² = -50 × 10^(-9) nC/m²

Charge density 2; σ2 = +25 nC/m² = +25 × 10^(-9) nC/m²

Now, formula for electric field strength is;

E = -(½ε)(|σ1| ± |σ2|)

ε is vacuum permittivity with a constant value as 8.85 × 10^(−12) C²/N.m²

|σ1| and |σ2| means we are taking the absolute values and would therefore not use the negative sign attached to them.

Now, in between x = 0 cm(0 m) and 50 cm (0.5 m), electric field generated by both charge densities would be in the same direction and thus;

E_in = -(½ε)(|σ1| + |σ2|)

E_in = -(½ × 8.85 × 10^(−12)) × [(50 × 10^(-9)) + (25 × 10^(-9))]

E_in = -4200 V/m

In contrast, when x ≥ 50 cm (0.5 m), electric field generated by both charge densities would be in opposite directions and thus;

E_out = -(½ε)(|σ1| - |σ2|)

E_out = -(½ × 8.85 × 10^(−12)) × [(50 × 10^(-9)) - (25 × 10^(-9))]

E_out = 1400 V/m

The magnitude of the potential difference from the origin to x = 80 cm(0.8 m) is calculated as attached;

From the attachment, we see that;

ΔV = 2520 V

what percentage is equal to 32/100 ​

Answers

32% I would guess ? :)

Answer:

32%

Step-by-step explanation:

32/100 is 32%

I need help please, can you help me?

Answers

Answer:

x= 16 degrees

Step-by-step explanation:

the angles can be a little hard to remember but just know that the angles that are outside of the transversal are exterior angles and if they are on the opposite sides of the line that passes through the parallel lines then they're alternate exterior angles and those angles that are inside are interior angles and if they are on the opposite sides of the line passing through the parallel then they are alternate interior angles .

$3,000 is invested in an account paying 4% interest and twice that amount is invested at 6%.

Which of the following expressions represents the amount of interest earned on the money invested at 6%?

a. 2(3,000)
b. 0.06(6,000)
c. 0.06(3,000)

Answers

Answer:

B

Step-by-step explanation:

The mapping below shows y as a function fo x?

True
False

Answers

Answer:

False

Step-by-step explanation:

x is the input and y is the output

the same input cannot have more than 1 output

-8 has 1 output

5 has 1 output

but "1" has 2 outputs

Please help anyone
Linear function f is shown in the graph. Write the slope-intercept form of the equation representing this function.

Answers

Y=3x-7 more characters because the app won’t let me put only the answer

The equation representing the function f(x) -

y = 4x - 8

We have a linear function f(x) as shown in the graph.

We have to determine the slope-intercept form of the equation representing this function.

What is the Slope - intercept form of the equation of a straight line ?

The Slope - intercept form of the equation of a straight line is as follows -

y = mx + c

where -

m - slope of line

c - intercept of line on y - axis.

According to the question, we have -

c = - 8 = intercept of line on y - axes.

Intercepting coordinates on  y - axes = (0, -8).

Intercepting coordinates on x - axes = (2, 0).

Slope = m = [tex]\frac{-8-0}{-2 -0}[/tex] = 4

Therefore, the equation representing the function f(x) -

y = 4x - 8.

To solve more questions on Straight lines, visit the link below -

brainly.com/question/28091452

#SPJ6

Ryan and two of his friends contribute $8.33 each, to buy a baseball bat from a sports shop. Find
the price of the baseball bat.

Answers

Answer:

24.99

Step-by-step explanation:

The price of the baseball bat is $24.99 :)

A line that passes through ( 3, 1) and 0,3 in y= mx+ b form

Answers

Answer:

y = -0.7x + 3

Step-by-step explanation:

I just used a math app called geo-gebra. Put the points in made a line and bam an answer. Hope this helps!

Evaluate the expression when c=5 and d=6.
7c+d.​

Answers

Answer:

41

Step-by-step explanation:

Step 1:

7c + d          Equation

Step 2:

7 ( 5 ) + 6      Input c and d

Step 3:

35 + 6       Multiply

Answer:

41          Add

Hope This Helps :)

u would have to plug in the numbers meaning

C=5 & D=6

so u would when they ask 7C+D u have to add parentheses for the numbers that are getting plugged in

7(5) + (6) = 41

M= 1/2
M= 2
M= -1/2
M=-2

Answers

Answer:

It should be 1/2

Step-by-step explanation:

the slope is =1/2 so the first option

Find the perimeter of the polygon with the vertices Q( – 3, 2), R(1, 2), S(1, - 2), and T (-3, -2).
, -2)

Answers

Answer:

Step-by-step explanation:

Kylie's family took a road trip to the Grand Canyon, Kylie fell asleep 42% of the way through the trip. If the total length of the trip was 600 miles, how many miles had they travelled when Kylie fell asleep?​

Answers

252 miles. Because just do 42% of 600.

any luck of help? I'll brainlist uu promise . I really need it for correction :)

Answers

Answer:

the cist of entry for x adults

Answer:

i think it would be d)

Step-by-step explanation:

cuz like, it says to write an expression. for an expression, most of the time you need more than one like number and variable

hope this helped :)

Alonso plans to buy a new kayak that costs $2,100. But he needs to pay a 8.5% tax. What is the total cost of the kayak?

Answers

Answer:

$ 2,273.25

Step-by-step explanation:

I do not understand this ​

Answers

Answer:

It would be C. The hexagon.

Answer:It would be C because you have 3 sides for the triangle than 4 sides for the rectangle, 5 sides for the pentagon, and 6 sides for the hexagon

Step-by-step explanation:

Is this graph of a function yes or no

Answers

Answer: It could be, just add two dots at the smiley face, BOOM! The function of Facial muscles in humans.

Step-by-step explanation:

It’s a functionnnnnnnnnnnnnnnnnnnn

What’s 19,975 divided by 25 show your work

Answers

the answer to the question is 799

Find the value of x and y given that p//q. Type answers alphabetically, and separate by a comma and a space

Answers

Answer:

39

Step-by-step explanation:

what is the value of the expression 12 - k
if k = (-3)

Answers

Answer:

15

Step-by-step explanation:

12-k

12- (-3)

12+3

=15

Answer:

15

Step-by-step explanation:

Substitute the variable, "k" into "12-k" from the equation "k=(-3).

12-k

12-(-3)

12+3---> two negatives make a positive

15

8. What is the result of (11x + 18i)(117 - 18i)?

Answers

1287x + 342 +(-198x + 2106) i
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