question_answer

The velocity of a body at time t = 0 is \[10\sqrt{2}\] m/s in the north-east direction and it is moving with an acceleration of 2 m/s2 directed towards the south.  The magnitude and direction of the velocity of the body after 5 sec will be                                     [AMU (Engg.) 1999]

A)             10 m/s, towards east

B)             10 m/s, towards north

C)             10 m/s, towards south

D)             10 m/s, towards north-east

Correct Answer: A

Solution :

              \[\overrightarrow{v}=\overrightarrow{u}+\overrightarrow{a}\,t\]\ \[v=\sqrt{{{u}^{2}}+{{a}^{2}}{{t}^{2}}+2u\,at\cos \theta }\]                         \[v=\sqrt{200+100+2\times 10\sqrt{2}\times 10\times \cos 135}\]\[=10\,m/s\] \[\tan \alpha =\frac{at\sin \theta }{u+at\cos \theta }\frac{10\sin 135}{10\sqrt{2}+10\cos 135}=1\]\\[\alpha =45{}^\circ \]                         i.e. resultant velocity is 10 m/s towards East.