It takes Ben 32 minutes to run 3 miles. At this rate, how long will it take him to run 8 miles?

A golfball is hit from the ground with an initial velocity of 200 ft/sec. The horizontal distance that the golfball will travel,

algol13

Answer:

The golfball launched with an initial velocity of 200ft/s will travel the maximum possible distance which is 1250 ft when it is hit at an angle of $\pi/4$ .

Step-by-step explanation:

The formula from the maximum distance of a projectile with initial height h=0, is:

$d(\theta)=\frac{v_i^2sin(2\theta)}{g}$

Where $v_i$ is the initial velocity.

In the closed interval method, the first step is to find the values of the function in the critical points in the interval which is $[0, \pi/2]$ . The critical points of the function are those who make $d'(\theta)=0$ :

$d(\theta)=\frac{v_i^2\sin(2\theta)}{g}\\d'(\theta)=\frac{v_i^2\cos(2\theta)}{g}*(2)\\d'(\theta)=\frac{2v_i^2\cos(2\theta)}{g}$

$d'(\theta)=0\\\frac{2v_i^2\cos(2\theta)}{g}=0\\\cos(2\theta)=0\\2\theta=\pi/2,3\pi/2,5\pi/2,...\\\theta=\pi/4,3\pi/4,5\pi/4,...$

The critical value inside the interval is $\pi/4$ .

$d(\theta)=\frac{v_i^2sin(2\theta)}{g}\\d(\pi/4)=\frac{v_i^2sin(2(\pi/4))}{g}\\d(\pi/4)=\frac{v_i^2sin(\pi/2)}{g}\\d(\pi/4)=\frac{v_i^2(1)}{g}\\d(\pi/4)=\frac{(200)^2}{32}\\d(\pi/4)=\frac{40000}{32}\\d(\pi/4)=1250ft$

The second step is to find the values of the function at the endpoints of the interval:

$d(\theta)=\frac{v_i^2sin(2\theta)}{g}\\\theta=0\\d(0)=\frac{v_i^2sin(2(0))}{g}\\d(0)=\frac{v_i^2(0)}{g}=0ft\\\theta=\pi/2\\d(\pi/2)=\frac{v_i^2sin(2(\pi/2))}{g}\\d(\pi/2)=\frac{v_i^2sin(\pi)}{g}\\d(\pi/2)=\frac{v_i^2(0)}{g}=0ft$

The biggest value of f is gived by $\pi/4$ , therefore $\pi/4$ is the absolute maximum.

In the context of the problem, the golfball launched with an initial velocity of 200ft/s will travel the maximum possible distance which is 1250 ft when it is hit at an angle of $\pi/4$ .

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3 years ago

The 40-ft-long A-36 steel rails on a train track are laid with a small gap between them to allow for thermal expansion. Determin

Oksana_A [137]

Answer:

um hola

Step-by-step explanation:

7 0

3 years ago

The length of a rectangle is 2x – 3 feet, and the width is 5 feet. What is the area of the rectangle in square feet?

drek231 [11]

5(2x - 3)

5 * 2x = 10x
5 * -3 = - 15

10x - 15

5 0

3 years ago

Read 2 more answers

Consider the function f whose graph is shown below.

cestrela7 [59]

Answer:

The domain of the function is [-9,7] and the range of the function is [-6,4]

6 0

3 years ago

A jet ski company charges a flat fee of $26 plus $3.25 per hour to rent a jet ski another company charges a fee of $24 plus $3.5

sladkih [1.3K]

Answer: 8 hours

Step-by-step explanation:

Company 1: 3.25x + 26

Company 2: 3.50x + 24

3.50x + 24 = 3.25x + 26

0.25x +24 = 26 subtracted 3.25x from both sides

0.25x = 2 subtracted 24 from both sides

x = 8 divided both sides by 0.25

Check:

Company 1: 3.25x + 26 = 3.25(8) + 26 = $52

Company 2: 3.50x + 24 = 3.50(8) + 24 = $52

6 0

3 years ago