Ask Question
3 January, 20:02

A man standing 9 feet from the base of a lamppost casts a shadow 6 feet long. if the man is 6 feet tall and walks away from the lamppost at a speed of 30 feet per minute, at what rate, in feet per minute, will his shadow lengthen?

+1
Answers (1)
  1. 3 January, 21:43
    0
    Let x be the distance of shadow and y the distance of the man from the lampost

    Height of lampost can be found using similar traingles and it comes to 15 feet.

    x / (x + y) = 6/15 = 2/5

    5x = 2x + 2y

    3x = 2y

    so y = (3/2) x and x = (2/3) y dy/dx = 3/2 and dx/dy = 2/3

    speed at which y is increasing = dy/dt = 30

    speed of shadow lengthening = dx / dt = dx/dy * dy/dt = 2/3 * 30 = 20 ft/min

    Answer is 20 ft / minute.
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “A man standing 9 feet from the base of a lamppost casts a shadow 6 feet long. if the man is 6 feet tall and walks away from the lamppost at ...” in 📙 Mathematics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers