question_answer

A projectile is projected at \[10\text{ }m{{s}^{-1}}\]cby making at an angle \[{{60}^{o}}\] to the horizontal. After some time its velocity makes an angle of \[{{30}^{o}}\] to the horizontal. Its speed at this instant is

A)  \[\frac{10}{\sqrt{3}}\]   

B)  \[10\sqrt{3}\]

C)  \[\frac{5}{\sqrt{3}}\]   

D)  \[5\sqrt{3}\]

Correct Answer: A

Solution :

:   Let \[\upsilon \] be the velocity of the projectile at P when it makes an angle \[{{30}^{o}}\] with the horizontal. Then \[\upsilon \,\cos {{30}^{o}}=u\cos {{60}^{o}}=10\times \frac{1}{2}=5\] \[\upsilon =\frac{5}{\cos {{30}^{o}}}=\frac{5}{(\sqrt{3}/2)}=\frac{10}{\sqrt{3}}m\,{{s}^{-1}}\]