The rear window in a car is approximately a rectangle, 1.3 m wide and 0.30 m high. The inside rear-view mirror is 0.50 m from the driver’s e

Question

The rear window in a car is approximately a rectangle, 1.3 m wide and 0.30 m high. The inside rear-view mirror is 0.50 m from the driver’s eyes and 1.50 m from the rear window. What are the minimum dimensions that the rear-view mirror should have if the driver is to be able to see the entire width and height of the rear window in the mirror without moving her head?

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Ngọc Hoa 4 years 2021-07-30T07:40:35+00:00 1 Answers 39 views 0

Answers ( )

  1. Adela
    0
    2021-07-30T07:41:45+00:00
    Reply

    Answer:

    Height of mirror 0.075 m


    width of mirror 0.325 m  

    Explanation:

    given data

    wide = 1.3 m

    high = 0.30 m

    driver’s eyes = 0.50 m

    rear window = 1.50 m

    solution

    we take here height / width of the mirror  is

    height / width   = \frac{h}{w}   ……………..1

    and

    height /width of the window is

    height /width  = \frac{h_w}{w_w}   ……………..2

    and

    distance of eye / window by the mirror is

    distance of eye / window = \frac{x_e}{x_w}      ……………..3

    so here

    θ = θi  = θr    ………………..4

    and  tanθ for vertical is

    tanθ  = \frac{h}{x_e}  

    tanθ  =  \frac{h_w}{(x_e + x_w)}       ………………..5

    so

    h =   h_w \times \frac{x_e}{(x_e + x_e)}     ………………..6

    put  here value and we get

    h = 0.30 \times \frac{0.50}{(0.50 + 1.50)}  

    h = 0.075 m

    and

    when we take here tanθ for horizontal than it will be

    tanθ = \frac{w}{x_e}    

    tanθ = \frac{w_w}{(x_e + x_w)}       …………………..7

    so

    w = w_w \times \frac{x_e}{(x_e + x_w)}         ………………..8

    put here value and we get

    w = 1.3 \times \frac{0.50}{(0.50 + 1.50)}  

    w = 0.325 m

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