Question

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 $3cm$ (given ${}_a{u}_{w}4/3$) :

• A. 12 $\sqrt{2}$ cm
• B. 16 cm
• C. 12 cm
• D. 8 cm

Answer 1

Answer: (C)

Here, $\angle PQN=45^{\circ }$
So, $PN=h\tan 45^{\circ }=32m$
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, $ON=h\tan r$
$=32\times \frac{3}{\sqrt{23}}=20cm$
$OP=PN-ON$
$=32-20=12cm$