The vertical distance from the dock to the bow is always 7, so, using the Pythagorean Theorem,
we get: 7^2 + B^2 = R^2 . Now we can take the derivative of this equation with respect to t: 2B
= 2R , which simplifies to B = R . We know that R = 25 and can use the Pythagorean
Theorem to find B: 7^2 + B^2 = 25^2 , so B = 24. Now we plug = −4, R = 25, and B = 24 into
the derivative and we get 24 = 25(−4). Now we can solve for : = − ft/s.
- ft/s
We are given the rate at which the woman is walking away from the street lamp and are looking
for the rate at which the length of her shadow is changing. It helps to draw a picture of the
situation.
If we label the distance between the woman and the street lamp, x, and the length of the
woman’s shadow, y, we can use similar triangles to get = . We can cross-multiply
and simplify.
