diffirential calculus
posted by kait .
a woman 6ft tall walks away from a light 10ft above the ground. if her shadow lengthens at the rate of 2ft/sec. how fast is she walking?

did you make a diagram?
let her distance from the lightpole be x ft
let the length of her shadow be y ft
by similar triangles ...
6/y = 10/(x+y)
6x + 6y = 10y
6x = 4y
6 dx/dt = 4 dy/dt
we are given: dx/dt + dy/dt = 2 ft/sec
dx/dt = 2  dy/dt
so
6(2  dy/dt) = 4 dy/dt
12  6dy/dt = 4dy/dt
12 = 10dy/dt
dy/dt = 12/10 = 1.2 ft/sec
Respond to this Question
Similar Questions

calculus
A woman 5.5 ft tall walks at a rate of 6 ft/sec toward a streetlight that is 22 ft above the ground. At what rate is the length of her shadow changing when she is 15 ft from the base of the light? 
calculus
A 6ft tall woman is walking away from a srteet lamp at 4 ft/sec that is 24ft tall. How fast is the length of her shadow changing? 
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 
Calculus rates
A man 6ft. tall walks at the rate of 5 ft/sec toward a streelight that is 16 ft. above the ground. At what rate is the length of his shadow changing when he is 10ft. from the base of the light? 
Math
a man 6ft tall walks at the rate of 5ft/sec toward a streetlight that is 16ft above the ground. At what rate is the length of his shadow changing when he is 10ft from the base of the light? 
Calculus
A woman 5 ft tall walks at the rate of 5.5 ft/sec away from a streetlight that is 16 ft above the ground. At what rate is the tip of her shadow moving? 
Calc
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? 
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? 
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? 
math
a man 1.9 meters tall walks away from a light 2.4m above the ground. if his shadow lengthens at a rate of 0.6 m/s, how fast is walking?