Question

On a rainy day in still air a motor cyclist riding towards North at 30 m suddenly breeze starts towards. West at 50 m/s. The apparent velocity with which the vehiclist will move is.

• A. $58.3{ms}^{-1}{tan}^{-1}\left(\frac{5}{3}\right)WofN$
• B. $65.4{ms}^{-1}NofW$
• C. $73.2{ms}^{-1}NofW$
• D. $53.8{ms}^{-1}{tan}^{-1}\left(\frac{3}{5}\right)WofN$

Answer 1

The correct option is D $53.8{ms}^{-1}{tan}^{-1}\left(\frac{3}{5}\right)WofN$

${\overrightarrow{v}}_{m,w}={\overrightarrow{v}}_{m,g}+{\overrightarrow{v}}_{w,g}$

$|{\overrightarrow{v}}_{m,w}|=\sqrt{({\overrightarrow{v}}_{mg}{)}^2+({\overrightarrow{v}}_{w.g})}$

$=\sqrt{2500+900}$

$=58.309m/s$

The angle made by the velocity is given as:

$\theta =ta{n}^{-1}\frac{v_c}{v_w}$

$⟹ta{n}^{-1}\frac{30}{50}$

$⟹ta{n}^{-1}\frac{3}{5}$ and it is in direction west of north