Problem 42.

A bicycle travels 3.2 km due east in 0.1 h, the 3.2 km at 15.0 degrees east of north in 0.21 h, and finally another 3.2km due east in 0.1 h to reach its destination. The time lost in turning is negligible. What is the average velocity for the entire trip?

Solution:

By definition the average velocity is equal to the ratio of the magnitude of the net displacement and the traveled time. The net displacement is shown in the figure.

We can find the x and y components of the vector of net displacement.

The x-component is

The y-component is

Then the magnitude of the net displacement is

The traveled time is 0.1 h + 0.21 h + 0.1 h = 0.41 h. Then the average velocity is