Question

A laser is placed in the center of a room with one mirrored wall and ceiling as shown. At what angle, θ, should the beam be pointed so that it impacts three quarters of the way up the right wall? The room is x = 4.70 m long, and  y = 3.60 m high.



[ans. 32.6 deg]

/θ

Question to be Graded Manually.

Answer 1

In angle OAB: tan theta = P/x/2 (1) In angle ODF: tan theta = y - p/q (2) In angle FEG, tan theta = y/4 (x - q) (3) 2p/x = y - p/q = y/4 (x - q) = k x = 2p/k y = qk + p} y = 4k (x - q) y = 4 kx - 4 kq qk + p = 4 kx - 4 kq 5 kq = 4 kx - p 5 kq = 7p k = 7/5 p/q x = 2p times 5q/7p x = 10 q/7 q = 3.29 m y = 12p/5 p = 1.5 m tan theta = 2p/x = 2 times 1.5/4.7 tan theta = 3/4.7 tan theta = 3/4.7 theta = 32.6 degree