Mathematics, 27.12.2019 00:31 TeeganGamil

Alight on the ground shines on a wall 20 meters away. if a man 2 meters tall walks from the light toward the wall at the rate 2.5 m/s, how fast is the length of his shadow decreasing when he is 10 meters away from the wall?

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Answer from: Alex4530

The height of the shadow is decreasing at the rate of $\frac{dy}{dt}=-1\:{\frac{m}{s} }$ .

Step-by-step explanation:

According with the graph (below) the small triangle (with the man as height), and the big triangle (with height along the wall) are similar, and hence the ratio of adjacent side length to opposite side length (with respect to the light) will be the same for both. This translates to

$\frac{x}{2}=\frac{20}{y} \\\\xy=40$

Differentiating this equation with respect to t, use the product rule, we get

$xy=40\\\\\frac{d}{dt}(xy)=\frac{d}{dt}(40)\\\\\frac{dx}{dt}y+x\frac{dy}{dt}=0$

We want to find how fast is the length of his shadow decreasing when the man is 10 meters away from the wall, so we solve for $\frac{dy}{dt}$

$\frac{dy}{dt}=-\frac{y}{x} \frac{dx}{dt}$

At the moment when the man is 10 meters from the wall, we have

x=20-10=10 ,

$\frac{dx}{dt} = 2.5 \:{\frac{m}{s} }$ ,

using the relation of similar triangles we can find y, $10y=40\\y=4$

$\frac{dy}{dt}=-\frac{4}{10} (2.5)=-1\:{\frac{m}{s} }$

The height of the shadow is decreasing at the rate of $\frac{dy}{dt}=-1\:{\frac{m}{s} }$ .

Alight on the ground shines on a wall 20 meters away. if a man 2 meters tall walks from the light to

Answer from: Quest

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

Answer from: Quest

to be honest i don't know but i need points so

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Alight on the ground shines on a wall 20 meters away. if a man 2 meters tall walks from the light to...