The velocities of two bodies A and B are given by $\vec{u_{1}} = 10 \hat{i} + 30 \hat{j} and \vec{u_{2}} = 5 \hat{i} - 10 \hat{j}$ . Match the following
Column-I Column-I
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

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

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

SCAN ME

	Column-I		Column-I
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