A man travels 7km due north,then 10km due east.find the resultant displacement.
d=sqrt(s₁²+s₂²) = sqrt(49+100) =12.2 km
To find the resultant displacement, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the displacement due north and due east form a right-angled triangle. We can consider the 7km due north as the vertical side (opposite angle θ) and the 10km due east as the horizontal side (adjacent to angle θ).
Using the Pythagorean theorem, we can calculate the resultant displacement (R) as follows:
R^2 = (7km)^2 + (10km)^2
R^2 = 49km^2 + 100km^2
R^2 = 149km^2
Taking the square root of both sides, we get:
R = sqrt(149km^2)
R ≈ 12.2km
Therefore, the resultant displacement is approximately 12.2km.