Monday

September 15, 2014

September 15, 2014

Posted by **Nikki** on Sunday, September 12, 2010 at 1:59pm.

A man 6ft tall walks away from a lamp post (15ft) at 5ft/sec. How fast is his shadow lengthening?

---

I have the picture, and the constants, the man and the lamp post. I have 5ft/sec as dw/dt, and I know I'm looking for ds/dt, the rate of the shadow.

Problem is, I don't know the actual equation to figure this out. Help please?

Thanks!

- Calculus -
**bobpursley**, Sunday, September 12, 2010 at 4:34pmThe lamp post makes a right triangle.

let x be the distance from the lamppost to the man (dx/dt=5; given) Let L be the length of is shadow, measured from the man feet to the end of the shadow.

(dL/dt is the rate of the shadow lengthens.

Using similar triangle

6/15=L/(L+x) or

6L+6x=15L

6x=9 L

x=3/2 L

dx/dt= 3/2 dL/dt

well, then dL/dt=2/3 dx/dt= 2/3 5=10/3 ft/sec

Now if you were to ask at what rate the shadow tip was moving , that is dx/dt+dL/dt

- Calculus -
**Heena Patel**, Tuesday, October 12, 2010 at 2:25pmlet x be the rate of shadow.

x / (x + 5) = 6 / 15

15x = 6(x+5) = 6x + 30

9x = 18

x = 30/9 = 10/3

**Answer this Question**

**Related Questions**

Calculus - Suppose a 6ft. man is 10 ft. away from a 24 ft. tall lamp post. If ...

calculus - A person 150cm tall is walking away from a lamp post at the rate of ...

calculus - My problem is that a stft above the sidewalk. a man 6ft tall walks ...

calculus - A 6ft tall woman is walking away from a srteet lamp at 4 ft/sec that ...

Math - a man 6ft tall walks at the rate of 5ft/sec toward a streetlight that is ...

diffirential calculus - a woman 6ft tall walks away from a light 10ft above the ...

Calculus - A man is 6ft tall and is walking at night straight toward a lighted ...

math - A man 6 feet tall walks at a rate of 5 feet/sec toward a street lamp that...

Calculus - A street light is at the top of a 17 ft tall pole. A woman 6 ft tall ...

Calculus - A street light is hung 18 ft. above street level. A 6-foot tall man ...