Physics

Problem

A bird leaves the top of a tree and flies with a constant speed of

15\,\text{m s}^{-1}

on a bearing of S

30^{\circ}

E (that is,

30^{\circ}

east of the south direction). (a) Express this direction as an angle measured anticlockwise from the positive

x

-axis (east). (b) Find the rectangular components of the bird’s velocity along the east–west (

x

) and north–south (

y

) axes. (c) Calculate the bird’s overall displacement vector after

20\,\text{s}

of flight, expressing your answer in component form as

\mathbf{r}=x\,\mathbf{\hat i}+y\,\mathbf{\hat j}

Intuitive explanation

Bearing problems blend navigation conventions with vector decomposition. The key is converting the compass direction into standard mathematical angle measurement (counterclockwise from east), then using $v_x = v\cos\theta$ and $v_y = v\sin\theta$ to find components. Once you have velocity components, displacement follows simply from $\mathbf{r} = \mathbf{v} \cdot t$ .

Intuitive explanation

Browse the problem library