Question

A bird moves with velocity 10m/s in the direction making an angle 60degree with the eastern line and 60degree verically upwards.Represent the velocity in rectangular form.

Answer 1

Bird's path make an angle of 60 degree with the eastern line, then it will make 30 degree with the vertical component.
Therefore,
$$\begin{gathered} \overrightarrow{\mathrm{v}}=\overrightarrow{{\mathrm{v}}_{\mathrm{x}}}\hat{\mathrm{i}}+\overrightarrow{{\mathrm{v}}_{\mathrm{y}}}\hat{\mathrm{j}} \\ \mathrm{Where}, \\ \mathrm{rectangular}\mathrm{components}\mathrm{are}, \\ {\mathrm{v}}_{\mathrm{x}}=\mathrm{v}\cos {60}^0=10\times \frac{1}{2}=5\mathrm{m}/\mathrm{s} \\ \mathrm{and}{\mathrm{v}}_{\mathrm{y}}=\mathrm{v}\sin {60}^0=\frac{10\times \sqrt{3}}{2}=5\sqrt{3} \end{gathered}$$