Posted by **Morgan** on Tuesday, June 18, 2013 at 3:25pm.

A street light is at the top of a 16ft tall pole. A woman 6ft tall walks away from the pole with a speed of 6ft/sec along a straight path. How fast is the tip of her shadow moving when she is 30ft from the base of the pole?

- Calc -
**Steve**, Tuesday, June 18, 2013 at 3:56pm
If the woman is x feet from the pole, and her shadow is of length s, then

s/6 = (x+s)/16

s/6 = x/16 + s/16

5/48 s = x/16

s = 3/5 x

So, unlike the problem where some angle is steadily changing, here the shadow is always 3/5 as long as the distance from the pole.

Since dx/dt = 6, ds/dt = 18/5

No matter how far she is from the pole.

However, that is not the answer to the question. The tip of her shadow is moving 18/5 from the woman. Add to that her own walking speed, and we see that the tip of the shadow is moving at 18/5 + 6 = 48/5 ft/s

## Answer This Question

## Related Questions

- calc related rates - A street light is at the top of a 18 ft tall pole. A woman ...
- Calculus - A street light is at the top of a 15 ft tall pole. A woman 6 ft tall ...
- calculus - A street light is at the top of a 13 ft tall pole. A woman 6 ft tall ...
- calculus - A street light is at the top of a 20 ft tall pole. A woman 6 ft tall ...
- calculus - A street light is at the top of a 16 ft tall pole. A woman 6 ft tall...
- calculus - A street light is at the top of a 15 ft tall pole. A woman 6 ft tall ...
- calculus - A street light is at the top of a 16 ft tall pole. A woman 6 ft tall...
- Calculus 1 - A street light is at the top of a 19 ft tall pole. A woman 6 ft ...
- calculus - A street light is at the top of a 17 ft tall pole. A woman 6 ft tall ...
- math - A street light is at the top of a 18 ft tall pole. A woman 6 ft tall ...

More Related Questions