calculus
posted by Anonymous .
A street light is at the top of a 16 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 4 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 30 ft from the base of the pole?

Let the woman be b feet from the pole, and let her shadow be a feet long.
Using similar triangles,
a/6 = (a+b)/16
so a = 3/5 b
da/dt = 3/5 db/dt = 3/5 * 4 = 12/5 ft/sec, a constant speed.
That seems odd. I expected her shadow's length to accelerate, but I don't see an error. These problems usually involve a steadily changing angle, and with the tangent function things speed up quickly. Not so here...
Respond to this Question
Similar Questions

math
A street light is at the top of a 18 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 8 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? 
calculus
A street light is at the top of a 17 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 6 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 40 ft from the base of the pole? 
Calculus 1
A street light is at the top of a 19 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 4 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 50 ft from the base of the pole? 
calculus
A street light is at the top of a 16 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 4 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 40 ft from the base of the pole? 
calculus
A street light is at the top of a 15 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 4 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 30 ft from the base of the pole 
calculus
A street light is at the top of a 19 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 5 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 40 ft from the base of the pole? 
calculus
A street light is at the top of a 20 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 6 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? 
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? 
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? 
Calculus
A street light is at the top of a 15 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 5 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 50 ft from the base of the pole?