Question

A bus travels 60km due north in 1 hour.It then travels 75km due east in 2 hours. What is the average velocity of the bus

Answer 1

By the definition of the average velocity, we have:

$$v_{avg}=\dfrac{d_{tot}}{t_{tot}}.$$

Let's find the total time:

$$t_{tot}=t_1+t_2=1\ h+2\ h=3\ h.$$

Let's write the resultant vector of the average velocity:

$$v_{avg}=(\dfrac{75}{3})i+(\dfrac{60}{3})j.$$

We can find the magnitude of the total displacement from the Pythagorean theorem:

$$d_{tot}=\sqrt{d_x^2+d_y^2}=\sqrt{(75\ km)^2+(60\ km)^2}=96\ km.$$

Therefore, the magnitude of the average velocity can be found as follows:

$$v_{avg}=\dfrac{96\ km}{3\ h}=32\ \dfrac{km}{h}.$$

We can find the direction of the average velocity as follows:

$$\theta=tan^{-1}(\dfrac{v_y}{v_x}),$$ $$\theta=tan^{-1}(\dfrac{60\ km}{75\ km})=38.6^{\circ}\ N\ of\ E.$$