Question

Martha is walking home from school. She walks 800 m down the road to a friend’s house. After finishing her homework, she walks back 300 m towards school to her house. What are the magnitudes of Martha’s displacement and distance from school to her home?

Answer 1

Martha's total distance from school to home is 1100 m, while her displacement to her home is 500 m in the direction away from school.

Step-by-step explanation:

When considering the problem where Martha is walking home from school, it's important to distinguish between the two concepts of distance and displacement in physics. Martha walks 800 m down the road to a friend's house and then walks back 300 m towards school to her own home. The total distance she covers is the sum of these two legs of her journey, which is 800 m + 300 m = 1100 m. However, displacement, which is a vector quantity, takes into account the direction of Martha's movement and the starting and ending points.

Since displacement is the straight-line distance from her starting point to her ending point with direction, we calculate Martha's displacement by taking the difference between her total path traveled away from school and back towards it. This means her displacement is 800 m - 300 m, which equals 500 m away from school. Thus, we can say Martha's displacement to her home is 500 m (in the direction away from school) and the magnitude of her displacement is also 500 m since displacement magnitude does not consider direction.