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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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Answer:

d_{b} = 2 d_{a}

Explanation:

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We substitute

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Let's apply this expression to our case, they indicate that the resistance of wire A is 4 times the resistance of wire B

    R_{a} = 4 R_{b}

We substitute

    ρ  4/π d_{a}² = 4 (ρ  4/π d_{b}²)

    1 / d_{a}² = 4 / d_{b}²

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4 0
3 years ago
What is the mass of an object that requires a force of 30 N to accelerate at a rate of 5 m/sec2 ?
Anastaziya [24]
M=F/A
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8 0
3 years ago
Consider a car travelling at 60 km/hr. If the radius of a tire is 25 cm, calculate the angular speed of a point on the outer edg
vlabodo [156]

To solve this problem it is necessary to apply the concepts given in the kinematic equations of movement description.

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Where,

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v = Lineal Velocity

R = Radius

At the same time we know that the acceleration is given as the change of speed in a fraction of the time, that is

\alpha = \frac{\omega}{t}

Where

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Our values are

v = 60\frac{km}{h} (\frac{1h}{3600s})(\frac{1000m}{1km})

v = 16.67m/s

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\omega = \frac{v}{R}

\omega = \frac{ 16.67}{0.25}

\omega = 66.67rad/s

Therefore the angular speed of a point on the outer edge of the tires is 66.67rad/s

At the same time the angular acceleration would be

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5 0
3 years ago
How much energy is used when a 110kw appliance is used for 3 hours
Bogdan [553]
We could take the easy way out and just say

(110 kW) x (3 hours) = 330 kilowatt hours .

But that's cheap, and hardly worth even 5 points.
If we want to talk energy, let's use the actual scientific unit of energy.
________________________________________________

" 110 kw " means 110,000 watts = 110,000 joules/second .

(3 hours) x (3600 sec/hour) = 10,800 seconds.

(110,000 joules/second) x (10,800 seconds) = 1.188 x 10⁹ Joules

 That's

==>  1,188,000,000 joules

==>  1,188,000 kilojoules

==>  1,188 megajoules

==>  1.188 gigajoules

Atsa nawfulotta energy ! 
It goes back to that "110 kw appliance" that we started with. 
That's no common ordinary household appliance.  110 kw is something like
147 horsepower.  In order to bring 110 kw into your house, you'd need to
take 458 Amperes through the 240-volt line from the pole.  Most houses
are limited to 100 or 200 Amperes, tops.  And the TRANSFORMER on
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6 0
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asambeis [7]

Complete Question:

Check the file attached to get the complete question

Answer:

In the film Ice word Revenge, vehicle 2 did not fall of the cliff because, Weight_{vehicle 1} < Weight_{vehicle 2} but in Claire's test, vehicle 2 off the cliff because Weight_{vehicle 1} \geq Weight_{vehicle 2}

Explanation:

In Claire's test, the weight of vehicle 1 is either equal to or greater than the weight of vehicle 2, so it was sufficient to push it down the cliff.  In the film Ice word revenge, the weight of vehicle 1 is less than the weight of vehicle 2, it is not sufficient to make it fall off the cliff ( Note: Looking exactly the same in the movie, as Claire claimed, does not mean they have the same mass). Therefore if Claire wants a collision that will not make the vehicle 2 fall off the cliff, he should collide it with a vehicle of lesser mass/weight.

8 0
3 years ago
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