/sci/ - Science & Math

Using some geometry, you can figure out that

<div class="math">\theta =arctan(\frac{x}{60})-arctan(\frac{60}{x})+\frac{\pi }{2}</div>

The length of arc D is <span class="math">D=60 \theta[/spoiler]

The position x is <span class="math">x=6t[/spoiler]. After two seconds, <span class="math">x=6(2)=12[/spoiler]

Plug this into the equation for D:

<div class="math">D =60 \left [ arctan(\frac{12}{60})-arctan(\frac{60}{12})+\frac{\pi }{2}\right ]\approx 23.687</div>

So the shadow moves about 23.687 ft.