A lamp is 3 metres high on a post located 5 metres from a vertical wall. A 2 metre tall man walks toward the wall from the lamppost on a path perpendicular to the wall. He is walking at a rate of 1 metre per second. When he is 1 metre from the wall, how fast is the shadow of his head moving up the wall?
A) 0.31 metres per second
B) 0.52 metres per second
C) 1.29 metres per second
D) 0.96 metres per second
E) 0.36 metres per second

Question

Quizplus · Accepted Answer

Explanation:The height of the man's head is 2 meters, and the distance from the lamppost to the wall is 5 meters. When the man is 1 meter from the wall, the distance from the lamppost to the man's head is 4 meters. The height of the shadow of the man's head is 3 meters, and the distance from the lamppost to the shadow of the man's head is 5 meters. When the man is walking at a rate of 1 meter per second, the distance from the lamppost to the man's head is decreasing at a rate of 1 meter per second. The height of the shadow of the man's head is increasing at a rate of 3/5 meters per second. Therefore, when the man is 1 meter from the wall, the shadow of his head is moving up the wall at a rate of 3/5 meters per second, which is approximately 0.6 meters per second.

A Lamp Is 3 Metres High on a Post Located