Question

A woman 5 ft tall walks at the rate of 7.5 ft/sec away from a streetlight that is 10 ft above the ground.

At what rate is the tip of her shadow moving?

At what rate is her shadow lengthening?

Answer 1

What next?

Answer 2

by similar triangles you have

Answer 3

$$
\Large{ \frac{10}{z} = \frac {5}{z-x}
\\10~(z-x) = 5z
\\ 10z - 10x = 5z
\\10z - 5z = 10x \\
\\ 5z = 10 x
\\ z = 2x \\ \therefore \\
\frac{dz}{dt} =2\frac{dx}{dt}

}
$$

Answer 4

Is dz/dt 7.5?

Answer 5

Or dx/dt?

Answer 6

dx/dt

Answer 7

So dz/dt is the answer??

Answer 8

Why is it 0.75, but not 7.5?

Answer 9

typo

Answer 10

dz/dt = 2*7.5

Answer 11

Is this the rate at which the tip of her shadow is moving?

Answer 12

yes

Answer 13

Then what about the rate at which the shadow is lengthening?

Answer 14

in our diagram, z - x is the length of the shadow

Answer 15

So it's 7.5

Answer 16

d/dt (z - x ) = dz/dt - dx/dt

= 2*7.5 - 7.5 = 7.5

Answer 17

yes thats correct

Answer 18

Ok awesome, it makes sense now. Thank you for your help!

Answer 19

:)