Question

A man has to go 50 m due north, then 40 m due east and then 20 m due south to reach a café from his home.
A. What distance does he have to walk to reach the café?
B. What is the displacement from his home to the café and find his speed and velocity?

Answer 1

A. We are given a situation in which man starts from his home and walks in different directions, to solve this problem the best situation will be to draw a free diagram representing the distance travelled and the directions of travel respectively.
B. Here, we need to tell the total distance, the net displacement, the speed and the velocity. We should remember that distance is a scalar quantity and displacement is a vector quantity. Speed is the rate of change of distance and velocity is the rate of change of displacement.

Complete step by step answer:

A. the man starts at O and the café is at C. so the total distance travelled to reach the café is (50+40+20) m =110m.
So, the man covers a total distance of 110 m.
B. displacement is the shortest path between the initial position and the final position. Initial position is at O and the final position is at C. so in the figure in right angled triangle we can use Pythagoras theorem to find the displacement,
${{h}^{2}}={{p}^{2}}+{{b}^{2}} \\\ \implies {{h}^{2}}={{40}^{2}}+{{30}^{2}} \\\ \implies h=\sqrt{2500} \\\ \therefore h=50 \\\$
So, the displacement comes out to be 50 m.

Note:
Speed is defined as the ratio of distance to the time while velocity is defined as the ratio of displacement covered to the total time taken, since, we are not provided with the time taken in the question we cannot find the speed and the velocity but we had found out the distance covered and the displacement of the body.