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Papessa [141]
3 years ago
5

A chimpanzee sitting against his favorite tree gets up and walks 70.9 m due east and 31.9 m due south to reach a termite mound,

where he eats lunch. (a) What is the shortest distance between the tree and the termite mound? (b) What direction does the shortest distance make, as a positive angle with respect to due east?
Physics
1 answer:
DIA [1.3K]3 years ago
4 0
A right triangle is formed by the 70.9 m walked east and 31.9 m walked south.
The legs of this right triangle are 70.9 and 31.9.
The shortest distance between two points is a straaight line. Therefore the hypotenuse of this triangle is going to be that shortest distance.
We can use the Pythagorean Theorem to find the hypotenuse of this triangle.
a^2+b^2=c^2\\70.9^2+31.9^2=c^2\\5026.81+1017.61=c^2\\6044.42=c^2\\c=\sqrt{6044.42}

c=\sqrt{6044.42}\approx\boxed{77.7458681}\ (decimal\ form)\\\\c=\sqrt{6044.42}=\sqrt{\frac{604442}{100}}=\boxed{\frac{\sqrt{604442}}{10}}\ (exact\ form)

As for the second part of the question, we want to find the angle formed by the hypotenuse and the 31.9 walked east.
We could use any of the three trigonometric ratios here since we know all 3 sides.
sine = opposite / hypotenuse
cosine = adjacent / hypotenuse
tangent = opposite / adjacent
I am going to use tangent, because then I won't have to deal with the hypotenuse and so the answer will be more accurate.

If you haven't already drawn yourself a diagram, now is a good time to.
The side opposite our angle is the 31.9, and the adjacent is 70.9.
Therefore, \tan(m\angle)=\frac{31.9}{70.9}.

We can use inverse trig ratios here to find the measure of our angle.
\tan^{-1}(\tan(m\angle))=\tan^{-1}(\frac{31.9}{70.9})\\\\m\angle=\tan^{-1}(\frac{31.9}{70.9})\approx\boxed{24.2243851\°\ or\ 0.422795279\ rad}
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An ice-making machine inside a refrigerator operates in a Carnot cycle. It takes heat from liquid water at 0.0 ∘C and rejects he
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Answer:

2.36 x 10^6 J

Explanation:

Tc = 0°C = 273 K

TH = 22.5°C = 295.5 K

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Use the Carnot's equation

\frac{Q_{H}}{Q_{c}}=\frac{T_{H}}{T_{c}}

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Answer:

The percentage power lost in the transmission line if the voltage not stepped up is 50%.

Explanation:

Given that,

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Using formula of power

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Where,I =current

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We need to calculate the percentage power lost in the transmission line

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P'=I^2\times R

Put the value into the formula

P'=(60)^2\times1

P'=3600\ W

The percentage power loss P''

P''=\dfrac{P'}{P}\times100=\dfrac{3600}{7200}\times100

P''=50\%

Hence, The percentage power lost in the transmission line if the voltage not stepped up is 50%.

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