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DedPeter [7]
3 years ago
12

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

t, the camera is closer to the left side of the field. The tension in the wire on the left is 1500 N, while the tension in the wire on the right is 800 N. Determine the length of each cable.
Mathematics
1 answer:
Katen [24]3 years ago
3 0

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.

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Answer:

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Step-by-step explanation:

With 15 balloons we make 1 poodle and 3 giraffes.  This means that 7,5 balloons were used to make 1 poodle, and other 7,5 balloons were used to make 3 giraffes.

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The dimensions of a square are altered so that 8 inches is added to one side while 3 inches is subtracted from the other. The ar
Alex_Xolod [135]

Answer

Find out the original side length of the square .

To prove

Let us assume that the original length of the square be x.

Formula

Area\ of\ rectangle = Length\times Breadth

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Step-by-step explanation:

The computation is given below:

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= 74 × 1.082856706

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