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A boat moves 4 m towards east and then 3 m north. The displacement and distance covered by the boat are:A. 7m,6m.B. 6m,5m.C. 5m,7m.D. 4m,3m.

Last updated date: 20th Jun 2024
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Hint:- The displacement is defined as the shortest distance between the initial and the final point of a travelling body. The distance is defined as the total path covered by the travelling body from initial and final point.
Formula used: The formula of the Pythagoras theorem is given by,
${H^2} = {P^2} + {B^2}$
Where H is the hypotenuse P is the perpendicular and B is the base of the triangle.

Complete step-by-step solution
In this problem it is given that the boat is moving 4 m in the
direction of east and the boat is also moving in the direction of north by 3 m and we need to find the distance and the displacement of the boat.

First of all let us calculate the value of distance travelled by the boat.
The distance in defined as the total distance travelled by the body and therefore the value of the distance travelled by the boat is equal to,
$\Rightarrow d = \left( {4 + 3} \right)m$
$\Rightarrow d = 7m$
Now let us calculate the displacement of the boat when the boat is moving 4 m in east direction and 3 m in the north direction.

Since displacement is the shortest distance between the initial and the final displacement.
Here the hypotenuse will give us the value of the displacement of the boat,
$\Rightarrow H = \sqrt {{4^2} + {3^2}}$
$\Rightarrow H = \sqrt {16 + 9}$
$\Rightarrow H = \sqrt {25}$
$\Rightarrow H = 5m$
The displacement is equal to$H = 5m$. The displacement is 5 m and distance is 7 m. the correct answer for this problem is option C.

Note:- The displacement of a travelling body will become zero if the initial and the final position of the body become same. The distance of a travelling body can never become zero as the total path travelled by the body is known as distance so even if the body comes to the initial position then the distance will have some positive value.