Question

A driver is moving on the car in the east direction with a velocity of 40m/s seems a bus moving in the north direction with the velocity of 70m/s what is the velocity of bus and in which direction

Answer 1

$$\begin{gathered} V_c=velocityofthecar=40m/s \\ {V}_{\mathbf{b}}=velocityofthebus \\ vistheresul\tan tvelocity=70m/s \\ v=\sqrt{{V_c}^2+{V_b}^2+2V_c{V}_b\cos \theta } \\ where\theta istheanglebetweencarandbus \\ nowresula\tan tvelocityismakinganangle90degreewithcar \\ \tan 90=\frac{V_b\sin \theta }{V_c+V_b\cos \theta } \\ therefore \\ {V}_c=-V_b\cos \theta \\ {v}_b=\frac{-V_c}{\cos \theta } \\ v=\sqrt{{V_c}^2+{V_b}^2+2V_c{V}_b\cos \theta } \\ 70=\sqrt{{40}^2+\frac{{40}^2}{{\cos }^2\theta }-2\times {40}^2} \\ \cos \theta =0.5 \\ \theta =60degree \\ {V}_b=\frac{-40}{0.5}=-80m/s \\ negatibesognshowsthatbusismovinginthedirection90+60=150degreewithrespecttocarwithspeed80m/s. \end{gathered}$$