Question

Joey drives his skidoo 7 kilometers north, then turns around and goes 4 kilometers south. What is his distance? What is his displacement?

a) Distance = 7 kilometers, Displacement = 3 kilometers north
b) Distance = 11 kilometers, Displacement = 7 kilometers north
c) Distance = 7 kilometers, Displacement = 11 kilometers north
d) Distance = 3 kilometers, Displacement = 7 kilometers north

Answer 1

11 kilometers is his distance and 3 kilometers north is his displacement.Thus option b is the correct answer.

Step-by-step explanation:

To find the distance traveled by Joey, we sum up the magnitudes of his displacements in each leg of the journey. He travels 7 kilometers north and then 4 kilometers south.

`\[ \text{Distance} = |7 \, \text{km}| + |4 \, \text{km}| = 11 \, \text{km} \]`

Now, to determine the displacement, we consider both magnitude and direction. Joey initially moves north by 7 kilometers and then south by 4 kilometers. The net displacement is the vector difference between these two movements.

`\[ \text{Displacement} = \sqrt{(7 \, \text{km})^2 + (-4 \, \text{km})^2} \]\[ \text{Displacement} = √(49 + 16) = √(65) \, \text{km} \]`

The direction of the displacement is north, as the initial movement is greater than the subsequent southward movement. Therefore, the final answer 11 kilometers is his distance and 3 kilometers north is his displacement.Thus option b is the correct answer.