Question

A cart travels 4 meters east and then 4 meters north.

Determine the magnitude of the cartâs resultant displacement

Answer 1

Displacement = √(4^2 + 4^2) = √(16 + 16) = √32 = 4√2 meters

Step-by-step explanation:

To determine the magnitude of the cart's resultant displacement, we can use the Pythagorean theorem. The Pythagorean theorem states that the square of the length of the hypotenuse (the displacement) of a right triangle is equal to the sum of the squares of the lengths of the other two sides.

We can imagine the cart's displacement as the hypotenuse of a right triangle, where one side is 4 meters (the eastward displacement) and the other side is 4 meters (the northward displacement). Using the Pythagorean theorem, we can calculate the magnitude of the displacement as follows:

Displacement = √(4^2 + 4^2) = √(16 + 16) = √32 = 4√2 meters

So the magnitude of the cart's resultant displacement is 4√2 meters.