Shadow Length and Rate of Change

This video tutorial explains a related rates problem involving a street light and a shadow. A 15-foot tall street light casts a shadow of a 6-foot tall woman walking away from it at 4 feet per second. The tutorial demonstrates how to calculate the rate at which the tip of her shadow moves away from her body and the pole when she is 45 feet from the pole. Using similar triangles, the video derives equations for ds/dt and dy/dt, solving them to find the rates of change.

What is the height of the street light in the problem?

• 25 feet

• 20 feet

• 10 feet

• 15 feet

How fast is the woman walking away from the pole?

• 4 feet per second

• 3 feet per second

• 5 feet per second

• 2 feet per second

What is the relationship between the woman's distance from the pole and the shadow length?

• x * s = y

• x - s = y

• x + s = y

• x = s

What is the simplified ratio of the sides of the similar triangles?

• 5:2

• 2:1

• 3:2

• 5:3

What is the equation derived for the shadow length s in terms of x?

• s = x

• s = 2/3 x

• s = 3/2 x

• s = x/2

What is the rate of change of the shadow length with respect to time?

• 8/3 feet per second

• 3 feet per second

• 4/3 feet per second

• 2 feet per second

Is the rate of change of the shadow length dependent on the woman's distance from the pole?

• Yes, it changes with distance

• No, it depends on the light's height

• No, it remains constant

• Yes, but only after 50 feet

What is the rate at which the tip of the shadow moves away from the pole?

• 15/3 feet per second

• 20/3 feet per second

• 10/3 feet per second

• 5/3 feet per second

What is the approximate speed of the shadow's tip moving away from the pole in decimal form?

• 6.67 feet per second

• 5.67 feet per second

• 8.67 feet per second

• 7.67 feet per second

What is the total distance from the pole to the tip of the shadow when the woman is 45 feet away?

• 65 feet

• 45 feet

• 50 feet

• 60 feet