Ask question

Ask question

All categories

3 years ago

5

During halftime of a football game, a slingshot launcher’s T-shirts at the crowd. A T-shirt is launch from a height of 3 feet wi

th an initial upward velocity of 64 ft./s. The T-shirt is caught at 45 feet above the field how long will it take the T-shirt to reach its maximum height? What is the maximum height? What is the range of the function of models the height of the T-shirt over time

1 answer:

Mrac [35]3 years ago

3 0

Answer:

Part A) The time it will take to the shirt to reach its maximum height is 2 seconds

Part B) The maximum height is 67 feet

Part C) The range is the interval [3,67]

$3\leq h\leq 67$

Step-by-step explanation:

In this problem we know that the equation is of the form

$h(t) = -16t^2 + v_0t + h_0$

where

-16 is the gravitational constant,

v₀ is the initial velocity in feet per second

h₀ is the initial height in feet

substitute the given values

$h(t) = -16t^2 + 64t + 3$

Part A) How long will it take the T-shirt to reach its maximum height?

we know that

The x-coordinate of the vertex is the time that it will take to the T-shirt to reach its maximum height

we have

$h(t) = -16t^2 + 64t + 3$

This is the equation of a vertical parabola open downward

The vertex represent a maximum

Convert the quadratic equation into vertex form

Factor -16

$h(t) = -16(t^2 -4t) + 3$

Complete the square

$h(t) = -16(t^2 -4t+4) + 3+64$

$h(t) = -16(t^2 -4t+4) + 67$

Rewrite as perfect squares

$h(t) = -16(t-2)^2) + 67$

The vertex is the point (2,67)

therefore

The time it will take to the shirt to reach its maximum height is 2 seconds

Part B) What is the maximum height?

we know that

The maximum height is equal to the y-coordinate of the vertex of the quadratic equation

The vertex is the point (2,67)

therefore

The maximum height is 67 feet

Part C) What is the range of the function of models the height of the T-shirt over time

we know that

The initial height is 3 feet, the maximum height is 67 feet and the T-shirt is caught at 45 feet above the field

so

The range is the interval [3,67]

$3\leq h\leq 67$

You might be interested in

Mrs. Bailey gives a test, and her students’ scores range from 30 to 70. She decides to curve the scores, so that they range from

Harman [31]

Answer:

f(x) = x*3/4 + 42.5

Step-by-step explanation:

The original difference between the pair is 70 - 30 = 40

The new difference between the pair is 95 - 65 = 30

Since the differences are not the same, Mrs Bailey must first perform a (slope) multiplication by a factor of 30/40 or 3/4

Then 30 * 3/4 = 22.5

Then she can shift the scores up by 65 - 22.5 = 42.5 in order to get the range from 65 to 95

Therefore, f(x) = x*3/4 + 42.5. We can test that

f(30) = 30*3/4 + 42.5 = 65

f(70) = 70*3/4 + 42.5 = 95

8 0

3 years ago

An athlete knows that when she jogs along her neighborhood greenway, she can complete the route in 10 minutes. It takes 20 minu

IgorLugansk [536]

Answer:

10 miles per hour.

Step-by-step explanation:

Let x represent athlete's walking speed.

We have been given that her jogging rate is 5 mph faster than her walking rate, so athlete's jogging speed would be $x+5$ miles per hour.

$\text{Distance}=\text{Rate}\cdot \text{Time}$

10 minutes = 1/6 hour.

20 minutes = 1/3 hour

While walking, we will get $D_{\text{walking}}=x\frac{\text{miles}}{\text{hour}}\cdot \frac{1}{3}\text{hour}$

$D_{\text{walking}}=\frac{x}{3}$

While jogging, we will get $D_{\text{jogging}}=(x+5)\frac{\text{miles}}{\text{hour}}\cdot \frac{1}{6}\text{hour}$

$D_{\text{jogging}}= \frac{(x+5)}{6}$

Since athlete is covering same distance while walking and jogging, so we can equate both expressions as:

$\frac{x}{3}=\frac{x+5}{6}$

Cross multiply:

$6x=3x+15$

$6x-3x=15$

$3x=15$

$\frac{3x}{3}=\frac{15}{3}\\\\x=5$

Therefore, athlete's walking speed is 5 miles per hour.

Jogging speed: $x+5\Rightarrow 5+5=10$

Therefore, athlete's jogging speed is 10 miles per hour.

3 0

3 years ago

What is 7/10+1/4 in simplest form

Stells [14]

Answer: 19/20

Step-by-step explanation:

7/10 turns into 14/20

1/4 turns into 5/20

14/20 + 5/20

14 + 5 over 20

= 19/20

19/20 is in simplest form.

3 0

3 years ago

Read 2 more answers

When converting between two measurement units, how can you tell which operation to use

german

Most of the time its juss common sense where you can point the right measurement with just sense i guess

7 0

3 years ago

Read 2 more answers

Solve These Number Patterns:

atroni [7]

1. times 2 but make it negative and then times 2 make it postiive.
-512,1024,-2048
2.Follows the same pattern

8 0

3 years ago