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2 months ago

11

In aviation, it is helpful for pilots to know the cloud ceiling, which is the distance between the ground and lowest cloud. The

simplest way to measure this is by using a spotlight to shine a beam of light up at the clouds and measuring the angle between the ground and where the beam hits the clouds. If the spotlight on the ground is 0.75 km from the hangar door. What is the cloud ceiling?

1 answer:

Sav [3.1K]2 months ago

4 0

Answer:

$b = a \frac{cos(\alpha)}{sin(\alpha)} = a Cot(\alpha)$

Explanation:

To find the height of the beam where it strikes the clouds, apply the Pythagorean theorem using these formulas:

$b = \sqrt[2]{H^{2} - a^{2}}$

$b = \sqrt[2]{H^{2} - H^{2} sin^{2} (\alpha)} \\b = H \sqrt[2]{1 - sin^{2} (\alpha)}$

If:

$H = \frac{a}{sin(\alpha)}$

Then:

$b = \frac{a}{sin(\alpha)} \sqrt{1 - sin^{2}(\alpha)}\\b = \frac{a}{sin(\alpha)} \sqrt{1 - 1 + cos^{2}(\alpha)}\\$

$b = \frac{a}{sin(\alpha)} \sqrt{cos^{2}(\alpha)}\\b = a \frac{cos(\alpha)}{sin(\alpha)} = a Cot(\alpha)$

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1 month ago

5. The speed of a transverse wave on a string is 170 m/s when the string tension is 120 ????. To what value must the tension be

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Answer:

The tension in the string when the speed increased is 134.53 N

Explanation:

Given;

Tension in the string, T = 120 N

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final speed of the transverse wave, v₂ = 180 m/s

The wave speed is expressed as;

$v = \sqrt{\frac{T}{\mu} }$

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29 days ago

A camera operator is filming a nature explorer in the Rocky Mountains. The explorer needs to swim across a river to his campsite

inna [3103]

Answer:

a. Angle= 28.82°

b. Approved. Although he might feel cold, he should be able to cross.

Explanation:

Velocity Vector

Velocity is a measure of how quickly something is moving in a specific direction. It is represented as a vector that has both magnitude and direction. If an object can only move in one direction, then speed can serve as the scalar equivalent of that velocity (only focusing on magnitude).

a.

The explorer aims to swim across a river to reach his campsite, as depicted in the image below. The river's velocity is vr and the explorer's swimming speed in still water is ve. If he were to swim straight towards the campsite, he would end up downstream due to the river's current. Therefore, he must swim at an angle that allows him to overcome the current while still moving towards his goal. This angle relative to the shore is what we need to determine. The explorer's speed can be broken down into its horizontal (vx) and vertical (vy) components. In order to counteract the river's flow:

$v_{ey}=v_r$

We can calculate the vertical component of the explorer's swimming speed as

$v_{ey}=|v_e|cos\alpha$

Thus

$v_r=|v_e|cos\alpha$

Finding the value of $\alpha$

$\displaystyle cos\alpha=\frac{v_r}{|v_e|}$

$\displaystyle cos\alpha=\frac{0.665}{0.759}=0.876$

Then the angle is given by

$\alpha=28.82^o$

b.

The component of the explorer's velocity that goes horizontally is

$v_{ex}=0.759sin28.82^o$

$v_{ex}=0.366\ m/s$

This represents the actual velocity directed towards the campsite

Considering that

$\displaystyle v=\frac{x}{t}$

To find t

$\displaystyle t=\frac{x}{v}$

Calculating the duration for the explorer to cross the river

$\displaystyle t=\frac{29.3}{0.366}$

$t=80\ sec$

As this time is under the hypothermia threshold (300 seconds), the conclusion is

Approved. Although he will feel cold, he should manage to cross successfully.

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