Solve and represent graphically, a rocket travels a distance of 4m south and 3m west, determine the magnitude
To determine the magnitude of the rocket's displacement, we need to calculate the length of the displacement vector using the Pythagorean theorem.
Let's represent the rocket's initial position as the origin (0, 0) on a coordinate plane. The rocket travels 4m south, which means it moves 4 units in the negative y-direction. Its final position will be (0, -4).
Then, the rocket travels 3m west, which means it moves 3 units in the negative x-direction. The final position will be (-3, -4).
Using the Pythagorean theorem, the magnitude of the displacement is given by:
magnitude = sqrt((change in x)^2 + (change in y)^2)
magnitude = sqrt((0 - (-3))^2 + (-4 - 0)^2)
magnitude = sqrt(3^2 + 4^2)
magnitude = sqrt(9 + 16)
magnitude = sqrt(25)
magnitude = 5
Therefore, the magnitude of the rocket's displacement is 5m.