Question

A man moves $4m$ along east direction, then $3m$ along north direction, after that he climbs a pole to a height of$12m$. Find the distance covered by him and his displacement.

Answer 1

The definition of distance and the definition of displacement can be used to calculate the answer for this problem. A distance is the total path travelled by a body between initial and final points. Displacement is the shortest distance covered by the body between the initial and final points.

Step by step solution:
As the distance is the total path travelled by the body and it is given that a man moves 4m along east direction then 3m along north direction and after that man climbs a pole 12m high. So here the total distance travelled by the man is given by,
$d = \left( {4 + 3 + 12} \right)m \\\ d = 19m \\\$
So the total distance covered by man is $d = 19m$.
Now, let us calculate the total displacement covered by the man. Before calculating the displacement by man we have to remember that the shortest distance between the initial and final position of man.

Here the man is moving 4m east after that he turns and walks 3m north and finally he climbs the pole so if we considered the initial position then the final position will be $3\hat i + 4\hat j + 12\hat k$ and the value of this displacement given by,
$s = \sqrt {{3^2} + {4^2} + {{12}^2}} \\\ s = \sqrt {9 + 16 + 144} \\\ s = \sqrt {169} \\\ s = 13m \\\$
So the displacement of the man is $s = 13m$.
The correct answer for this problem is distance $d = 19m$ and displacement of the man is $s = 13m$

Note: The final position of the man is at the top of the pole and the initial position is at the starting of the travel so the horizontal shortest distance is from the initial position and the point where the pole is fixed and then the vertical distance travelled by man is the height of the pole so if we consider the overall motion then it forms a triangle with base as the horizontal distance i.e. OB and the perpendicular as the height of the pole i.e. 12m and the hypotenuse as the initial position and the top of the pole as the final point.
So the value of OB is $OB = 5m$, $BC = 12m$and after applying the Pythagoras theorem the value of OC comes out to be $BC = 13m$.