A 1.7m lady is walking away from an 8.3m streetlamp at a rate of 1.3m/s. How fast is the tip of the shadow cast in front of her moving along the ground when she is 9.0m from the post?

Answer 1

Let x is distance from the post to tip of shadow. Then for similarity of triangles we have:

x/(x - 1.3t) = 8.3/1.7; 1.7x = 8.3(x - 1.3t); 8.3x - 1.7x = 14.11t; 6.6x = 14.11t; x = 2.138t

dx/dt = 2.138 m/s