Question

A lamp is located on the ground 10m from a building. A person 2m tall walks from thelighttowardthebuildingatarateof2m/s. Findtherateatwhichtheperson’sshadow on the wall is shortening when the person is 5m from the building.

Answer 1

x distance from light
2/x = h/10
at t = 0, x = 5 so h = 4
dx/dt = 2 given
so
x = 5 + 2 t
dx = 2 dt

h = 20/x = 20/(2t+5)
dh/dt = -20(2)/(2t+5)^2
=-20/(25) = -4/5 = -0.8 m/s