The velocities of two bodies A and B are given by $\vec{u_{1}} = 10 \overset{\land}{i} + 30 \overset{\land}{j}$ And $\vec{u_{2}} = 5 \overset{\land}{i} - 10 \overset{\land}{j}$ . Match the following
Column - I Column - II
a The magnitude of velocity of A is e 25 units
b The magnitude of velocity of B is f $5 \sqrt{65} units$
c The magnitude of Relative velocity of A with respect to B g $5 \sqrt{5} units$
d The magnitude of Resultant velocity of A and B is h $10 \sqrt{10} units$
a b c d
1 h g f e
2 f h e g
3 f e h g
4 g e h f

Moderate

Solution

$u_{1} = \sqrt{10^{2} + 30^{2}} = 10 \sqrt{10} u n i t s u_{2} = \sqrt{5^{2} + 10^{2}} = 5 \sqrt{5} u n i t s {\vec{u}}_{12} = {\vec{u}}_{1} - {\vec{u}}_{2} = 5 \hat{i} + 40 \hat{j} \Rightarrow u_{12} = \sqrt{5^{2} + 40^{2}} = 5 \sqrt{65} u n i t s N o w, {\vec{u}}_{1} + {\vec{u}}_{2} = 15 \hat{i} + 20 \hat{j} \Rightarrow |{\vec{u}}_{1} + {\vec{u}}_{2}| = \sqrt{15^{2} + 20^{2}} = 25 u n i t s$

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	Column - I		Column - II
a	The magnitude of velocity of A is	e	25 units
b	The magnitude of velocity of B is	f	$5 \sqrt{65} units$
c	The magnitude of Relative velocity of A with respect to B	g	$5 \sqrt{5} units$
d	The magnitude of Resultant velocity of A and B is	h	$10 \sqrt{10} units$