1. ## Related Rates

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 2.5 m/s, how fast is the length of his shadow on the building decreasing when he is 4 m from the building? (Round your answer to two decimal places.)

using similar triangles:

y/12 = 2/12-x

y = 12 / 12-x

y = 24 (12-x)^-1

dy/dt = -24(12-x)^-2 (-dx/dt)

dy/dt = 24(dx/dt) / (12-x)^2

Given:

dy/dt = ?
dx/dt = -2.5
x = 4

Plug in:

dy/dt = 24(-2.5) / (12-4)^2

dy/dt = -.9375

dy/dt = -.94

Web assigned marked my final answer wrong.

Thanks.

2. ## Re: Related Rates

Originally Posted by NeoSonata
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 2.5 m/s, how fast is the length of his shadow on the building decreasing when he is 4 m from the building? (Round your answer to two decimal places.)

using similar triangles:

y/12 = 2/12-x

y = 12 / 12-x

y = 24 (12-x)^-1

dy/dt = -24(12-x)^-2 (-dx/dt)

dy/dt = 24(dx/dt) / (12-x)^2

Given:

dy/dt = ?
dx/dt = -2.5
x = 4

Plug in:

dy/dt = 24(-2.5) / (12-4)^2

dy/dt = -.9375

dy/dt = -.94

Web assigned marked my final answer wrong.