Question

A person walks 45 m East and then walks 39 m at an angle 40◦ North of East. What is the magnitude of the total displacement? Answer in units of m.

Answer 1

Answer:

r = 78.95 m

Explanation:

given,

Person Walk in east, r₁ = 45 m

Then he walk, r₂= 39 m in the direction of 40◦ North of East.

writing the total displacement in x- direction

 r₁ₓ  = 45 m

 r₂ₓ = 39 cos 40°

  r₂ₓ = 29.87 m

total displacement in x-direction

rₓ = r₁ₓ + r₂ₓ

rₓ = 45 + 29.87

rₓ = 74.87 m

displacement in y-direction

r_{1y} = 0 m

r_{2y} = 39 sin 40°

r_{2y} = 25.07 m

total displacement in y- direction

  r_y = 25.07 m

using Pythagoras theorem for the magnitude calculation

 $r = \sqrt{r_x^2 + r_y^2}$

 $r = \sqrt{74.87^2 +25.07^2}$

        r = 78.95 m

The magnitude of total displacement is equal to 78.95 m.