Friday

March 27, 2015

March 27, 2015

Posted by **Anonymous** on Tuesday, October 23, 2012 at 4:47pm.

- Calculus -
**bobpursley**, Tuesday, October 23, 2012 at 5:36pmMake the diagram. The streetlight height is 16. Let the distance from the streetlamp base to the tip of the shadow as x. Label the distance from the streetlamp base to the person as d.

Similar triangles:

16/x=5/(x-d)

5x=16x-16d

11x=16d

11 dx/dt=16 dd/dt

dd/dt =5.5ft/sec, solve for dx/dt

- Calculus -
**Reiny**, Tuesday, October 23, 2012 at 5:51pmI do not agree with bobpursley's solution

let the distance of the woman from the streetlight be x ft

let the length of her shadow be y ft

by ratios ...

5/y = 16/(x+y)

16y = 5x + 5y

11y = 5x

11 dy/dt = 5 dx/dt

but dx/dt = 5.5

dy/dt = (5/11)(5.5) = 2.5

So her shadow is lengthening at 2.5 ft/sec

but she is moving at 5.5 ft/sec, so her shadow is moving at 2.5+5.5 or 8 ft/sec

( I am walking along the inside of a moving train at 3 ft/sec, while the train is moving at 50 ft/sec

So I am moving at 53 ft/sec)

- Calculus -
**Calc**, Tuesday, October 23, 2012 at 9:36pmReiny is definitely correct.

**Answer this Question**

**Related Questions**

calculus - A woman 5.5 ft tall walks at a rate of 6 ft/sec toward a streetlight ...

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

Calculus - Shadow Length A man 6 feet tall walks at a rate of 3 ft per second ...

calculus - A street light is at the top of a 19 ft tall pole. A woman 6 ft tall ...

Calculus ~ Related Rates - A man 2 meters tall walks at the rate of 2 meters per...

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

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

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

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

Calculus - A light is hung 15 ft above a straight horizontal path. If a man 6 ft...