Duffy was analyzing the trajectory made after throwing a football. his coach was able to measure that his throw reached a maximum height of 18 feet after 2 seconds. he figured that the ball left his hand at a height of 5 feet. Let the independent variable represent time and the dependant variable represent height of the ball. Use this information to write an equation to model the path of the ball and predict when the ball will hit the ground the ball will hit the ground at approximately ________ seconds

Answers

Answer 1

Answer:

Answer:

4.35 seconds.

Step-by-step explanation:

Let x represent the time the independent variable and y be dependent variable (height of the ball).

We are told that Duffy figured that the ball left his hand at a height of 5 feet. This means at x equals 0, y was 5 or initial height of ball is 5 feet.

We have been given that Duffy's coach measured that his throw reached a maximum height of 18 feet after 2 seconds. This means that at x equals 2 y was 18.

As point (2,18) represents maximum height of ball, so it will be vertex of parabola.

Since initial height of ball is less than maximum height, so our parabola will be downward opening and leading coefficient will be negative.

We know that vertex form of a downward opening parabola is in form: $y=-a(x-h)^2+k$

$y=-a(x-2)^2+18$

Let us find value of a using point (0,5).

$5=-a(0-2)^2+18$

$5=-a*4+18$

$5-18=-a*4+18-18$

$-13=-4a$

$(-13)/(-4)=(-4a)/(-4)$

$(13)/(4)=a$

Therefore, the equation $y=-((13)/(4))(x-2)^2+18$ can be used to find the height of ball after x seconds.

To find the time it will take the ball to hit the ground, we will substitute y equals 0 in our equation.

$0=-((13)/(4))(x-2)^2+18$

$0-18=-((13)/(4))(x-2)^2+18-18$

$0-18=-((13)/(4))(x-2)^2$

$-18*((4)/(13))=-(x-2)^2$

$(72)/(13)=(x-2)^2$

Taking square root of both sides of our equation we will get,

$\sqrt{(72)/(13)}=x-2$

$x-2\pm 2.35339$

$x-2=2.35339\text{ (or) } x-2=2.35339$

$x-2+2=2.35339+2\text{ (or) } x-2+2=-2.35339+2$

$x=4.35339\text{ (or) } x=-0.35339$

$x\approx 4.35\text{ (or) } x\approx -0.35$

Since time can not be negative, therefore, the ball will hit the ground approximately after 4.35 seconds.

Related Questions

Their are 41 stickers she put them in 7 equal groups how many groups are their
How could you change the equation here so it has infinitely many solutions? What would infinitely many solutions mean in terms of the situation? If the equation were 6x + 2 = 5x + 17 would there be one unique solution? What is it, and what would it mean in terms of the situation
I don't understand why I keep getting the answer 934.64 for 160.8 X 44.3
Let each square represent 1/3 unit by 1/3 unit
A+63 b+52c equal if a=6, b=51 and c=1/4

The quadratic function below represents a parabola that opens down. Which value could be the missing number in the equation ? The missing coefficient could be ?

Answers

Answer:

-4

Step-by-step explanation:

The direction of the parabola depends on the sign of the leading coefficient i.e. sign of the coefficient with the squared term.

Remember these two points for vertical parabola:

If the leading coefficient is positive the parabola will always open upwards
If the leading coefficient is negative the parabola will always open downwards

We are given that the parabola opens down. This means that the leading coefficient must be negative. Among the given options only one option contains a negative number i.e. -4.

Therefore, the missing coefficient could be -4

Can the mean have a remainder?

Answers

Yes the mean can have a remainder but the remainder would normally be either rounded or converted into a fraction.

Anthony made a chicken dish for dinner. He added a 10 -oz package of vegetables and a 14- oz package of rice to 40 oz of chicken. what was the total weight of the chicken dish in pounds

Answers

You would need to add 10 -oz with 14-oz and once you get that answer,you need to add it to 40-oz

If 40+10+14=64 and there are 16 oz in q pound then 64/16=4 so 4 pounds

If 12% is 36 then what is 100%

Answers

100 % would be the greatest number your using, from 1 to 100 100% would be 100

What is 6m+10=46
What is the m?

Answers

Answer:

m = 6

Step-by-step explanation:

6m + 10 = 46

6m = 46 - 10

6m = 36

m = 36 : 6

m = 6

The answer is 6.....since 6x6is 36 and 36+10=46

A sporting goods store charges $30 for 12 cans of tennis balls and $45 for two boxes of golf balls. A coach orders 100 cans of tennis balls and 5 boxes of golf balls. How much will the coach pay for the tennis and golf balls?

Answers

tennis ball
12 cans = $30
1 can = $ 30/12 = $2.5

golf balls
2 boxes = $45
1 box = $45 /2 = $ 22.5

100 cans of tennis balls + 5 boxes of golf boxes
(100 * $ 2.5) + ( 5 * $ 22.5)
$250 + $112.5
$362.5

Other Questions

What is 13/6 as a mixed number

If a bird flies 4 hours, it can travel 15 miles. How many minutes doe sit take that bird to fly 90 miles? (PLEASE SHOW STEPS!)

How to solve 6w 30; 5, 6, 7

McKenzie works for a catering company.She is making ice tea for an upcoming event. For each container of tea she uses 16 tea bags and 3 cups of sugar. If McKEnzie uses 64 tea bags, how many cups of sugar will she use?