Question

A spotlight on the ground shines on a wall 12 m away. If a man 2 m tall walks from the spotlight toward the building at a speed of 1.3 m/s, how fast is the length of his shadow on the building decreasing when he is 4 m from the building?

Answer 1

Im not a pro in related rates but I think you use similar triangles. I can't really hep any further as related rates are a weakness.

Answer 2

how do you set up related rates though?>

Answer 3

Let s is the shadow of the man,
and d is the distance from the man to the spotlight
d' = 1.3 m/sec at d = 12 - 4 = 8
From similar triangle: s/ 2 = 12/ d
-> s = 24/d
=> s' = - 24 d'/ d²
= - 24 * 1.3 / 64 = - 0.49 m/s