Question

A car is moving towards east with a speed of $25km{h}^{-1}$. To the driver of the car, a bus appears to move towards north with a speed of $25\sqrt{3}km{h}^{-1}$. What is the actual velocity of the bus?

• A. $50km{h}^{-1},{30}^{\circ }E$ of $N$
• B. $50km{h}^{-1},{30}^{\circ }N$ of $E$
• C. $25km{h}^{-1},{30}^{\circ }E$ of $N$
• D. $25km{h}^{-1},{30}^{\circ }N$ of $E$

Answer 1

The correct option is A $50km{h}^{-1},{30}^{\circ }E$ of $N$

${\overline{v}}_c=25\hat{i},{\overline{v}}_{b/c}=25\sqrt{3}\hat{j}$

${\overline{V}}_{b/c}={\overline{V}}_b-{\overline{V}}_c\Rightarrow {\overline{V}}_b={\overline{V}}_{b/c}+{\overline{V}}_c$

$\Rightarrow {\overline{v}}_b=25\hat{i}+25\sqrt{3}\hat{j}$

$|{\overline{v}}_b|=\sqrt{{25}^2+(25\sqrt{3}{)}^2}=50km{h}^{-1}$

$\tan \theta =\frac{25}{25\sqrt{3}}=\frac{1}{\sqrt{3}}\Rightarrow \theta ={30}^o$