Question

15. A body is simultaneously given two velocities, one 10m/s due east and other 20m/s due north-west. calculate the resultant velocity.

Answer 1

Let the body has given two velocities A and B. So,
A = 10 m/s
B = 20 m/s
Here, velocity A is due east and velocity B is due north-east. So, the angle between these two force will be,
$\theta ={90}^o+{45}^o={135}^o$
Thus, the resultant velocity, $R=\sqrt{A^2+B^2+2AB\cos \theta }$

$$\begin{gathered} =\sqrt{{10}^2+{20}^2+2\times 10\times 20\cos {135}^o} \\ =\sqrt{500+400\times \left(-\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\sqrt{2}$}\right.\right)} \\ =\sqrt{217.156} \\ =14.74m/s \end{gathered}$$