An important strength of the naturalistic observation method of research is that

A man walks along a straight path at a speed of 4 ft/s. A searchlight is located on the ground 6 ft from the path and is kept fo

BARSIC [14]

We are given that,

$\frac{dx}{dt} = 4ft/s$

We need to find $\frac{d\theta}{dt}$ when $x=8ft$

The equation that relates x and $\theta$ can be written as,

$\frac{x}{6} tan\theta$

$x = 6tan\theta$

Differentiating each side with respect to t, we get,

$\frac{dx}{dt} = \frac{dx}{d\theta} \cdot \frac{d\theta}{dt}$

$\frac{dx}{dt} = (6sec^2\theta)\cdot \frac{d\theta}{dt}$

$\frac{d\theta}{dt} = \frac{1}{6sec^2\theta} \cdot \frac{dx}{dt}$

Replacing the value of the velocity

$\frac{d\theta}{dt} = \frac{1}{6} cos^2\theta (4)^2$

$\frac{d\theta}{dt} = \frac{8}{3} cos^2\theta$

The value of $cos \theta$ could be found if we know the length of the beam. With this value the equation can be approximated to the relationship between the sides of the triangle that is being formed in order to obtain the numerical value. If this relation is known for the value of x = 6ft, the mathematical relation is obtained. I will add a numerical example (although the answer would end in the previous point) If the length of the beam was 10, then we would have to

$cos\theta = \frac{6}{10}$

$\frac{d\theta}{dt} = \frac{8}{3} (\frac{6}{10})^2$

$\frac{d\theta}{dt} = \frac{24}{25}$

Search light is rotating at a rate of 0.96rad/s

4 0

3 years ago

When two mechanical waves have a displacement in opposite directions, and they overlap, what will the resulting wave look like a

Sophie [7]

The second one is the answer

5 0

4 years ago

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Do you think the amount of positive charge on the glass after rubbing it with silk cloth will be equal to the amount of negative

IrinaK [193]

This is not a answer but can’t you just search that up on the internet and get the answer?

5 0

3 years ago

Which explanation of the solar system best fits the observations of the planets and how they orbit the sun?Question options:The

diamong [38]

<h2>Answer: The planets formed at the center of a collapsing spinning cloud of gas and dust.</h2>

The most accepted theory so far, in relation to the formation of our solar system is that it was originated by the contraction of a cloud of interstellar gas due to its own gravity.

To understand it better:

According to this theory, a cloud of gas and interstellar dust began to shrink due to its own gravity. This led to the increase in the temperature of the system, which began to rotate forming a large gas sphere in the center (the Sun) with a flat disk around it.

This is how the Sun formed from the sphere in the center and the planets formed from the disk orbiting in the same plane.

6 0

4 years ago

A chemical form in which most fat exists in food as well as in the body is known as ______________.

ehidna [41]

It is known as chelesterol

5 0

4 years ago

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