A beacon is flashing on top of a 50 foot tower. A 6 foot tall man walks constantly away from the tower at 5 feet/sec. At the ins

Question

zzz [600]

2 years ago

11

A beacon is flashing on top of a 50 foot tower. A 6 foot tall man walks constantly away from the tower at 5 feet/sec. At the ins

tant the man is 30 feet away from the tower, what rate is the tip of his shadow moving away from the tower

Mathematics

1 answer:

Viefleur [7K] · Answer 1 · 2023-02-28T06:32:43+03:00

Answer: $\frac{253}{44}$

Step-by-step explanation:

ignore the "at the instant the man is 30 feet away" part, set it as X and the man's shadow as Y.

Similar triangles so we can do $\frac{50}{x+y} = \frac{6}{y}$ .

Solve for it we get 44y = 6x

Differentiate relative to time t, we get 44y' = 6x'.

change in x (x') is equal to 5. And we get the answer y' = $\frac{33}{44}$ .

the $\frac{33}{44}$ ft/sec is the rate of which the length of the shadow is changing. add 5 to it for the rate of the tip of his shadow moving away from the tower.