Question

After a long day of driving you take a light night swim in a swimming pool in your hotel. When you go to your room you find that you have lost the key of your room in the pool. You borrow flash light from the hotel manager and work around the pool, shining light light into it. The light shine on the key which is lying at surface and is directed at the bottom of the pool when the flash light is held 1.2m above the surface a horizontal distance of 1.5 m from the edge. Water is 4m deep.
How far is the key from the edge of the pool?

• A. 4m
• B. 4.16 m
• C. 4.86 m
• D. 4.36 m

Answer 1

The correct option is D 4.36 m

$\tan i=\frac{1.5}{1.2}=\frac{5}{4}$
$\sin i=\frac{5}{\sqrt{41}}$
$\sin r=\frac{5}{\sqrt{41\times }\frac{4}{3}}=\frac{15}{4\sqrt{41}}$
$\tan r=\frac{x}{4}=\frac{15}{\sqrt{431}}\Rightarrow x=2.86m$
$x=1.5+2.86=4.36m$