posted by opy on .
A man of height 1.8m walks away from a lamp at a height of 6m. If the man's speed is 7m/s, find the speed in m/s at which the tip of the shadow moves.
draw a right triangle: vertical 6m, horizontal leg x
Now within that triangle, another vertical 1.8 m, and the horizontal distance to the lamppost is L, so the length to the tip of shadow is x-L
given: dL/dt=7, solve for dx/dt
h=1.8 m, H=6 m, v=7 m/s u=?
x is the distance of man to lamp post,
y is the distance from the tip of the shadow to the lamp post.
From the similar triangles
H/h = y/(y-x),
6/1.8 = y/(y-x),
4.2 y=6 x,