A body is simultanceously given two velocities : one ` 12 ms^(-1)` due East and other ` 5 ms^(-1)` due North. Find the resultant velocity.

Explanation

Here, ` v_1 = 12 ms^(-1)` , v_2 =5 ms^(-1) , theta= 90^@` .
Resulat velocity, ltbbrgt ` v = sqrt (v_1^2 + v_2^2+ 2 v_1 v_2 cos 90^@)`
` = sqrt (v_1^2 +v_1^2) = sqer ( 12^2 + 5^2 ) = 13 ms^(-1~)
Let resultanct velocity ` vec v` make and angle ` beta` the east direction, then
` tan beta = ( v-2 sin 90^@)/( v-1 +v_2 cos 90^@) = v^@/v_1 = 4/(12) =0 .4167`
`= tan 22^@ 37'` ltbRgt ` beta= 22^@ 37' ` (North of east).