a spotlight on the ground is shining on a wall away. if a woman tall walks from the spotlight toward the building at a speed of how fast is the length of her shadow on the building decreasing when she is from the building?

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24-10-2022
Physics

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a spotlight on the ground is shining on a wall away. if a woman tall walks from the spotlight toward the building at a speed of how fast is the length of her shadow on the building decreasing when she is from the building?

Answer :

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RioSengupta RioSengupta · Answer 1 · 2022-11-04T09:46:14-04:00

His shadow is shortening at a rate of dy/dt = 0.6m/s at the time.

What is triangle total degrees?

The triangle's three angles add up to a total of 180 degrees

The individual is standing at point D and has his head at point E at the time indicated in the problem.

At that moment, his shadow is visible on the wall at y = BC.

The two right triangles ABC and ADE both contain similar triangles. The ratios on their respective sides in the similar triangles are equal:

AD/AB = DE/BC

8/12 = 2/y

y = 3

If we suppose that the man is x distance from the building, then the distance from the spotlight to the man is 12 x.

12-x/12 = 2/y

1-1/12x = 2 1/y

Let's take derivatives of both sides:

-1/12dx = -2 .1/y²dy

Divide both sides by dt as follows.

-1/12.dx/dt = 2/y²dy/dt

At the time specified:

dx/dy = 1.6m/s

y = 3

Let's connect them

- 1/2 (1.6) = -2.9 dy/dt

dy/dt = 1.6/12×9/2 = 0.6m/s.

At the time in question, this is the pace at which his shadow's length is shortening.

To know more about triangles visit:

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The complete question is:

"A spotlight on the ground shines on a wall 12 m away. If a man 2 m tall walks from the spotlight toward the building at a speed of 1.6 m/s, how fast is the length of his shadow on the building decreasing when he is 4 m from the building?"