A person whose eyes are H = 1.59 m above the floor stands L = 2.29 m in front of a vertical plane mirror whose bottom edge is 43 cm above the floor, What is the horizontal distance x to the base of the wall supporting the mirror of the nearest point on the floor that can be seen reflected in the mirror?
2007-05-30 14:00:19 · 4 answers · asked by Anonymous in Science & Mathematics ➔ Physics
This is easy if you draw it out.
If the person's eyes are 1.59m above the floor and the bottom of the mirror is 0.43m above the floor, then the person's eyes are 1.59-0.43=1.16m above the bottom of the mirror.
If you draw a right triangle perpendicular to the plane of the mirror, you get the horizontal leg equal to 2.29m (the distance of the person from the mirror) and a vertical leg equal to 1.16m (the distance we just calculated).
When light bounces off a mirror, the incoming angle (measured from the perpendicular to the mirror) is the same as the outgoing angle. In other words, if the light hits the mirror head on (perpendicular) it bounces right back to the source. If it comes in at a 10 degree angle to the perpendicular, it comes off at 10 degrees.
So, let 'A' be the angle between the line from the person's eyes to the bottom of the mirror and the perpendicular to the mirror itself.
Looking at the sketch you've (hopefully :p) been drawing, you have a horizontal leg equal to 2.29m, a vertical leg equal to 1.16m, and an angle A.
From basic trig, sin A = 1.16/2.29, or A = 30.43 deg.
The light bounces off the bottom of the mirror until it hits the floor. The light-floor-mirror triangle is similar to the triangle we just used, so sin A = 0.43m/x
Or, x = 0.43/sin 30.43 = 0.85m
Hope this helps.
2007-05-30 14:28:30 · answer #1 · answered by lango77 3 · 0⤊ 1⤋
Using a little bit of geometry and the Thales theorem (absolutely no barbaric trig, which gives an elegant and easy solution), I got the following relation:
(2.29+x)/1.59 = x/0.43
I let you solve the equation to find x (it's easy), but here is the explanation; get a piece of paper and a pencil, that will help.
Thales involves 2 triangles, right?
The nearest point on the floor that can be seen reflected in the mirror has an image in the mirror that is behind the wall. This point behind the wall, the eye and the feet form one triangle. The other triangle is the same image behind the wall, the bottom of the mirror and the bottom of the wall. There you have your 2 triangles.
Thales theorem says that ratio of the distance x (which is also the distance from the wall to the image behind the wall) by the height of the mirror is the same as the ratio of the total distance from the feet to the image behind the wall divided by
the height (eye-feet distance).
In terms of math, what I just said is nothing but the equation up there, which I let you work out. After all, it's your homework/exam...
2007-05-30 14:18:35 · answer #2 · answered by Damien 4 · 0⤊ 1⤋
i do not imagine the different 2 solutions are fairly ideal. you should use the Pythagorean theorem. (a^2+b^2=c^2) The x displacement is (60 + eighty) cm, and the y displacement is 40 cm: sqrt((60+eighty)^2+40^2)=one hundred forty 5.602cm
2016-10-18 11:38:16 · answer #3 · answered by ? 4 · 0⤊ 0⤋
We were doing a problem just like that in math the other day. Ehhh sorry I forgot how to do it though. =[
2007-05-30 14:10:29 · answer #4 · answered by Katie L 2 · 0⤊ 1⤋