14 is a blank of 7 and 14

A 140 kg camera is suspended by two wires over a 40 metre wide football field to get shots of the action from above. At one poin

Katen [24]

Answer:

Please red the answer below

Step-by-step explanation:

In order to determine the length of each cable you use the Newton second law for each component of the forces involved in the situation.

For the x component you have:

$T_1cos\theta_1-T_2cos\theta_2=0$ (1)

T1: tension of the first cable = 1500N

T2: tension of the second cable = 800N

θ1: angle between the horizontal and the first cable

θ2: angle between the horizontal and the first cable

For the y component you have:

$T_1sin\theta_1+T_2sin\theta_2-W=0$ (2)

W: weight of the camera = Mg = (140kg)(9.8m/s^2) = 1372N

You can squared both equations (1) and (2) and the sum the two equations:

$T_1^2cos^2\theta_1=T_2^2cos^2\theta_2\\\\T_1^2sin^2\theta_1=T_2^2sin^2\theta_2-2WT_2sin\theta_2+W^2$

Then, you sum the equations:

$T_1^2(cos^2\theta_1+sin^2\theta_1)=T_2^2(sin^2\theta_2+cos^2\theta_2)-2Wsin\theta_2+W^2$ (3)

Next, you use the following identity:

$sin^2\theta+cos^2\theta=1$

and you obtain in the equation (3):

$T_1^2=T_2^2-2WT_2sin\theta_2+W^2\\\\sin\theta_2=\frac{T_2^2-T_1^2+W^2}{2WT_2}=\frac{(800N)^2-(1500)^2+(1372N)^2}{2(800N)(1372N)}=0.066\\\\\theta_2=sin^{-1}0.066=27.23\°$

With this values you can calculate the value of the another angle, by using the equation (1):

$\theta_1=cos^{-1}(\frac{T_2cos(27.23\°)}{T_1})=cos^{-1}(\frac{(800N)(cos27.23\°)}{1500N})\\\\\theta_1=61.69\°$

Now, you can calculate the length of each cable by using the information about the width of the football field. You use the following trigonometric relation:

$l_1cos\theta_1=40-d\\\\l_2cos\theta_2=d\\\\$

d: distance to the right side of the field

By using the cosine law you can fins a system of equation and then you can calculate the values of l1 and l2.

3 0

3 years ago

What is the slope of the line that passes through the points (-9,0) and (-17 , 0 )

marishachu [46]

Answer:

$\mathrm{Slope=== > 0}$

Step-by-step explanation:

Hi student, let me help you out!

<u></u>

First, let's recall the slope formula: $\boxed{\mathrm{\cfrac{y2-y1}{x2-x1}}}}$ , where y2 and y1 are y-coordinates; x2 and x1 are x-coordinates.

Plugin the values: $\mathrm{\cfrac{0-0}{-17-(-9)}}$ .

Upon simplifying, we obtain $\mathrm{\cfrac{0}{-17+9}}$ .

Upon simplifying this further, we obtain $\mathrm{\cfrac{0}{-9}}$ .

0 divided by anything results in 0.

✨ ∴, the slope of this particular line is 0, and this line looks something like this: $\rule{200}{1}$ .

See, it's a horizontal line, with a rise of 0, meaning that it goes up 0 units.

Hope this helped you out! Ask in comments if even the slightest queries arise.

Best Wishes!

$\star\bigstar\underline{\underline{\overline{\overline{\textsf{Reach far. Aim high. Dream big.}}}}}\bigstar\star$

$\underline{\rule{300}{5}}$

4 0

2 years ago

I need the help on this

Salsk061 [2.6K]

Answer:

Go catipiller

Step-by-step explanation:

8 0

3 years ago

The side of a equilatoral triangle is 9.9 cm. find its perimetre

tia_tia [17]

The perimeter is the distance all the way around.

That's the sum of all the sides.

A triangle has 3 sides.

In an equilateral triangle, they're all the same length.

If one of them is 9.9 cm, then all of them add up to (3) · (9.9 cm) .

3 0

3 years ago

Read 2 more answers

Show and explain how you found the answer to this problem. Carla has 152 pictures to put in a scrapbook. If she can fit 12 pictu

jekas [21]

Explanation:

You make the equation. If she can put 12 on each page then you would multiply 12 by p (pages) and have it equal to 152

152=12p

To solve this, you would divide 12 from both sides

152/12=12.666

Therefore, 12.6=pages but since there aren’t 12.6 pages and you need to keep it a whole number you would round up to 13 because if you kept it at twelve pages you would have those pictures left over.

7 0

3 years ago

Read 2 more answers