A particle possesses two velocities at the same time one 4 m/s due south and other the 2√2 m/s due - Physics - Motion In A Plane

Question

A particle possesses two velocities at the same
time one 4 m/s due south and other the 2√2 m/s due north-
east Find the magnitude and direction of resultant
velocity

Jyoti Pant · Accepted Answer

Here u=4m/s,v= $2 \sqrt{2} m / s$

Components of velocity v along east and north are $v \cos 45 = 2 \sqrt{2} \times \frac{1}{\sqrt{2}} = 2 m / s v \sin 45 = 2 \sqrt{2} \times \frac{1}{\sqrt{2}} = 2 m / s S o, n e t v e l o c i t y t o w a r d s n o r t h v_{n o r t h} = 2 - 4 = - 2 m / s v_{e a s t} = 2 m / s T h e r e s u l \tan t v e l o c i t y v = \sqrt{{(- 2)}^{2} + 2^{2}} = \sqrt{8} m / s = 2 \sqrt{2} m / s N o w f o r d i r e c t i o n, l e t θ b e t h e a n g l e w h i c h t h e r e s u l \tan t m a k e s w i t h t h e e a s t d i r e c t i o n \tan θ = \frac{- 2}{2} = - 1 θ = \tan^{- 1} (- 1)$

A particle possesses two velocities at the same time one 4 m/s due south and other the 2√2 m/s due north- east. Find the magnitude and direction of resultant velocity.