Question

a lantern is placed on the ground 100 feet away from a wall. A man six feet tall is walking at a speed of 10 feet/second from the lantern to the nearest point on the wall. When he is midway between the lantern and the wall, the rate of change in the length of his shadow is what?

Answer 1

Answer:

Step-by-step explanation:

At midway man is 50 ft away from lantern & wall

height of man = 6ft

Distance from lantern = 50 ft

Tanθ = 6/50

=> tanθ = Shadow/100

=> 6/50 = Shadow/100

=> Shadow = 12 ft

time taken to cover 50 feet = 50/10 = 5 sec

Rate of change in length of shadow = 12/5 = 2.4 ft