Posted by **sh** on Tuesday, December 1, 2009 at 11:18pm.

A man 2m tall walks away from a lamppost whose light is 5m above the ground. If he walks at a speed of 1.5m/s, at what rate is his shadow growing when he is 10m from the lamppost?

I tried to draw a diagram, but I don't understand where the 5m is, the height of the lamppost? Is the question asking for the derivative of the speed?

- Calculus -
**Reiny**, Tuesday, December 1, 2009 at 11:33pm
draw a lamppost, vertical line, and label it 5 m high (we assusme the light is at the top of the lamppost)

draw a horizontal line, the sidewalk? , and draw the man , vertical line, somewhere on the sidwalk.

Join the top of the lamppost to the man's head and continue until you hit the sidewalk.

label the distance between the post and the man as y, label the length of his shadow x

we are given dy/dt as 1.5 m/s, we are to find dx/dt when y = 10 m

I see to right-angled triangles, with a smaller inside a larger.

By similar triangles:

5/(x+y) = 2/x

cross-multiply, ...

5x = 2x + 2y

3x = 2y

differentiate with respect to t

3dx/dt = 2dy/dt

dx/dt = 2(1.5)/3 = 1 m/s

Notice we did not need the 10 m, there was no place to sub it in.

We have shown that the man's shadow is growing at a constant rate of 1 m/s, no matter where he is.

Be careful with this question.

Had it asked "how fast is the man's shadow moving", we would have to add the man's speed to the 1 m/s for a speed of 2.5 m/s.

- Calculus -
**Reiny**, Tuesday, December 1, 2009 at 11:41pm
My goodness!

I just noticed that I typed "to" instead of "two" in "I see to right-angled triangles ..."

- Calculus -
**sh**, Tuesday, December 1, 2009 at 11:45pm
Thank you so much for clearing it up showing the steps crystal clear. How do you know that 1.5m/s is dy/dt?

- Calculus -
**Anonymous**, Saturday, August 16, 2014 at 7:54am
2.5 km/h

## Answer this Question

## Related Questions

- Calculus - Shadow Length A man 6 feet tall walks at a rate of 3 ft per second ...
- Calculus - A man standing 9 feet from the base of a lamppost casts a shadow 6 ...
- Calculus - A street light is hung 18 ft. above street level. A 6-foot tall man ...
- calculus - My problem is that a stft above the sidewalk. a man 6ft tall walks ...
- algebra - A man is walking away from a lamppost with a light source h = 6 m ...
- precalculus - A man is walking away from a lamppost with a light source h = 6 m ...
- Calculus- rates - A man 6ft. tall walks at the rate of 5 ft/sec toward a ...
- diffirential calculus - a woman 6ft tall walks away from a light 10ft above the ...
- calculus - A 6-foot man walks away from a 16-foot lamppost at a speed of 5 ft/...
- Calculus - A bright light on the ground illuminates a wall 12 meters away. A man...

More Related Questions