# Calculus

posted by .

A street light is hung 18 ft. above street level. A 6-foot tall man standing directly under the light walks away at a rate of 3 ft/sec. How fast is the tip of the man's shadow moving?

I know I would've to set up a proportion.

18 / 6 = x + y / y

x = distance of man from light
x + y = tip of shadow

• Calculus -

You mean
18 / 6 = (x + y) / y
we know dx/dt, we need dy/dt
then the tip moves at dx/dt + dy/dt

18 y = 6x + 6 y
12 y = 6 x
12 dy/dt = 6 dx/dt
dy/dt = .5 dx/dt
so dy/dy = 3/2 = 1.5
and the sum
3+1.5 = 4.5 ft/sec

• Calculus -

Okay, I see what I did wrong. I did dy/dt = 6 instead of dy/dt = .5. Thanks a lot

• Calculus -

x = distance of man from base of light

y/(y+x) = 6/18
Solve for y
18y = 6(y + x)
18y = 6y + 6x
12y = 6x
y = 6/12 x = 1/2 x

Find dy/dx of 1/2 x
dy/dx = 1/2

Find derivative with respect to t
dy/dt = 1/2 dx/dt

x is increasing 3 ft/sec
dx/dt = 3 ft/sec
dy/dt = 1/2 dx/dt
dy/dt = 1/2 (3)
dy/dt = 3/2 = 1.5 ft/sec

Shadow moving at the rate of 1.5 ft/sec

• Calculus -

A street light is at the top of a 13 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 7 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 35 ft from the base of the pole?

## Similar Questions

1. ### calculus

My problem is that a stft above the sidewalk. a man 6ft tall walks away from the light at the rate of 3ft/sec. at what rate is his tip of shadow moving
2. ### Calculus

A street light is at the top of a 19 foot tall pole. A 6 foot tall woman walks away from the pole with a speed of 7 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 30 feet from the base of the pole?
3. ### calculus

A street light is mounted at the top of a 6-meter-tall pole. A man 2 m tall walks away from the pole with a speed of 1.4 m/s along a straight path. How fast is the tip of his shadow moving when he is 16 m from the pole?
4. ### calculus

A street light is mounted at the top of a 15-ft-tall pole. A man 6 ft tall walks away from the pole with a speed of 7 ft/s along a straight path. How fast is the tip of his shadow moving when he is 45 ft from the pole?
5. ### Calculus

A light is hung 15 ft above a straight horizontal path. If a man 6 ft tall is walking away from the light at the rate of 5 ft/sec, how fast is his shadow lengthening and at what rate is the tip of the manâ€™s shadow moving?
6. ### math

A street light is at the top of a 16.0 ft. tall pole. A man 5.9 ft tall walks away from the pole with a speed of 5.5 feet/sec along a straight path. How fast is the tip of his shadow moving when he is 47 feet from the pole?
7. ### calculus

A 5.5 foot tall woman walks at 6ft/s torward a street light that is 16.5 ft above the ground. what is the rate of change of the length of her shadow when she is 14ft from the street light?
8. ### Calculus

A street light is at the top of a 14.5 ft. tall pole. A man 5.3 ft tall walks away from the pole with a speed of 5.5 feet/sec along a straight path. How fast is the tip of his shadow moving when he is 47 feet from the pole?
9. ### Related Rates

A street light is at the top of a 10.5 ft. tall pole. A man 5.4 ft tall walks away from the pole with a speed of 3.5 feet/sec along a straight path. How fast is the tip of his shadow moving when he is 47 feet from the pole?
10. ### math

A street light is at the top of a 11 ft. tall pole. A man 6.2 ft tall walks away from the pole with a speed of 4.5 feet/sec along a straight path. How fast is the tip of his shadow moving when he is 31 feet from the pole?

More Similar Questions