Q. A stone lies at the bottom of a stream. A boy wants to hit it with a stick. Taking aim the boy holds the stick in the air at an angle of $ 45^{\circ} $ . At what distance from the stone will the stick hit the bottom. If the depth is $3\, cm$ (given $ _{a}{u}_{w} 4/3$) :
Haryana PMTHaryana PMT 2000
Solution:
Here, $\angle P Q N=45^{\circ}$
So, $P N=h \tan 45^{\circ}=32 m$
Now, $ \mu=\frac{\sin i}{\sin r} $
So, $ \sin r=\frac{\sin i}{\mu} $
or $\sin r=\frac{\sin 45^{\circ}}{(4 / 3)}=\frac{3}{4 \sqrt{2}} $
$\tan r=\frac{\sin r}{\cos r}=\frac{\sin r}{\sqrt{1-\sin ^{2} r}}$
$=\frac{3 / 4 \sqrt{2}}{\sqrt{1-\frac{9}{32}}}=\frac{3}{\sqrt{23}} $
So, $ON = h \,\tan r$
$ =32 \times \frac{3}{\sqrt{23}}=20 \,cm$
$ O P=P N-O N $
$=32-20=12 \,cm$
