question_answer

A truck travelling due north at 20 m/s turns west and travels at the same speed. The change in its velocity be [UPSEAT 1999]

A)                 40 m/s N?W

B)                             \[20\sqrt{2}\,\]m/s N?W

C)                 40 m/s S?W       

D)                 \[20\sqrt{2}\] m/s S?W

Correct Answer: D

Solution :

                    From figure \[{{\overrightarrow{v}}_{1}}=20\hat{j}\] and \[{{\overrightarrow{v}}_{2}}=-20\hat{i}\]                 \[\Delta \overrightarrow{v}={{\overrightarrow{v}}_{2}}-{{\overrightarrow{v}}_{1}}=-20(\hat{i}+\hat{j})\]                 \[|\Delta \overrightarrow{v}|\,=\,20\sqrt{2}\]and direction                 \[\theta ={{\tan }^{-1}}(1)=45{}^\circ \] i.e. S?W