Question

An ant walks on a piece of graph paper straight along the x axis a distance of 10.0 cm in 2.20 s . It then turns left 30.0 ∘ and walks in a straight line another 10.0 cm in 1.80 s . Finally, it turns another 70.0 ∘ to the left and walks another 10.0 cm in 1.40 s .

a)Determine the x component of the ant's average velocity.

b)Determine the y component of the ant's average velocity.

c) Determine the magnitude of ant's average velocity.

d) Determine the direction of ant's average velocity. (

counterclockwise from x axis )

Answer 1

$\hat{i},\hat{j}$ are unit vectors along positive X and positive Y axes respectively.

$\overrightarrow {OA}=10\hat{i}$

$\overrightarrow {AB}=10(\cos30\degree\hat{i}+\sin30\degree \hat{j})$

Vector BC makes an angle $30\degree+70\degree=100\degree$ with the positive X-axis.

$\overrightarrow {BC}=10(\cos100\degree\hat{i}+\sin100\degree \hat{j})$

Average velocity = total displacement / total time

$\vec{v}_{avg}=\frac{10\hat{i}+10(\cos30\degree\hat{i}+\sin30\degree \hat{j})+10(\cos100\degree \hat{i}+\sin100\degree\hat{j})}{2.20+1.80+1.40}$

$\vec{v}_{avg}=\frac{16.924\hat{i}+14.848\hat{j}}{5.40}$

$\vec{v}_{avg}=3.13\hat{i}+2.75\hat{j}$

a) X-component of ant's average velocity ${v}_{avg,x}=3.13\,cm/s$

b) Y-component of ant's average velocity ${v}_{avg,y}=2.75\,cm/s$

c)Magnitude of ant's average velocity ${v}_{avg}=\sqrt{3.13^2+2.75^2}=4.17\,cm/s$

d)Direction of ant's average velocity $\theta=\tan^{-1}\left ( \frac{2.75}{3.13} \right )=41.3\degree$ counter-clockwise from Positive X-axis.