Laws Of Motion Question 258
Question: 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]
Options:
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
Show Answer
Answer:
Correct Answer: A
Solution:
$ \overrightarrow{v}=\overrightarrow{u}+\overrightarrow{a}t $
$ v=\sqrt{u^{2}+a^{2}t^{2}+2uat\cos \theta } $
$ v=\sqrt{200+100+2\times 10\sqrt{2}\times 10\times \cos 135} $
$ =10m/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.
