Posted by AH on .
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?
make a sketch
label the man's distance from the post as x
and the length of his shadow y
by similar triangles and ratios
6/y = 15/(x+y)
15y = 6x + 6y
9y = 6x
3y = 2x
3dy/dt = 2dx/dt
dy/dt = (2/3)(7) = 14/3 ft/s
so the length of his shadow is lengthening at 14/3 ft/s
but it is moving at 14/3 + 7 or 35/7 ft/sec
Thank you very much!
By the way, 14/3+7 equals 35/3, not 35/7.