# A large van has a velocity 30m/s at $20^{\large\circ}S$ of E in still air.A gust of wind of 20m/s due East relative to the Earth strikes the van.What is the resultant velocity of the van relative to the Earth,during the gust

$\begin{array}{1 1}49.3\;ms^{-1},\quad 12^{\circ}\; \text{S of E}\\28.19\;ms^{-1},\quad 16^{\circ}\; \text{S of E}\\10.26\;ms^{-1},\quad 22^{\circ}\; \text{S of E}\\48.19\;ms^{-1},\quad 44^{\circ}\; \text{S of E}\end{array}$

## 1 Answer

Answer : $49.3\;ms^{-1},\quad 12^{\circ}\; \text{S of E}$
$v_{vE}=\sqrt{v_{vEx}^2+v_{vEy}^2}=\sqrt{48.19^2+(-10.26)^2}$
$\theta=\tan^{-1}\big(\large\frac{v_{vEy}}{v_{vEx}}\big)$$=\tan^{-1}\big(\large\frac{-10.26}{48.19}\big)$$=12.0^{\large\circ}$ S of E
answered Aug 13, 2014

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