Into the light!

Classical Mechanics Level 2

As shown in the diagram above, there is a light source at a height of $H$ , and a man of height $h$ walks toward it with constant velocity $v$ .

Photons hit the road (which is made of mirror) at point $P$ and reflects into the man's eye (approximated by a point-like photoreceptor located exactly at the height $H$ above the ground).

Due to the motion of the man, the location of $P$ moves toward the light with velocity $u$ .

Find the ratio $\dfrac{v}{u}$ .

Details and Assumptions:

Take $H:h = 3:1$ .
Give your answer to 3 decimal places.

The answer is 1.333.

1 solution

Steven Chase
Nov 6, 2016

We have $\begin{aligned} v &= \frac{dx}{dt}, \\ \\ \tan\theta = \frac{H}{p} &= \frac{h}{x-p} \\ H(x-p) &= hp. \end{aligned}$ Since $H = 3h,$ $\begin{aligned} H(x-p) = 3h(x-p) &= hp \\ 3x - 3p &= p \\ p &= \frac{3x}{4} \\ \implies u &= \frac34 \frac{dx}{dt}. \end{aligned}$ Therefore, $\frac{v}{u} = \frac43.$

Nicely done... :)

Tahmid Ranon - 4 years, 7 months ago

Into the light!

The answer is 1.333.

1 solution

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