To get to school, a girl walks 1 km North in 15 minutes. She then walks 200 m Southwest in 160 seconds. What is the girl’s average velocity for her walk to school?

Answer 1

To find the girl's average velocity, we need to calculate the total displacement and total time elapsed.

The first part of her walk covers 1 km North, which is a displacement of +1 km.

The second part of her walk covers 200 m Southwest, which can be broken down into horizontal and vertical components. The horizontal component is 200 * cos(45 degrees) = 141.42 m, and the vertical component is 200 * sin(45 degrees) = 141.42 m. Since the direction is Southwest, both components are negative. Therefore, the displacement in this part is -141.42 m in the horizontal direction and -141.42 m in the vertical direction.

The total displacement is then 1 km North – 141.42 m West – 141.42 m South, which simplifies to -0.14142 km South.

The total time elapsed is 15 minutes + 160 seconds, which can be converted to 15 minutes + (160/60) minutes = 15 minutes + 2.67 minutes = 17.67 minutes.

The girl's average velocity is displacement/time = (-0.14142 km South) / (17.67 minutes) = -0.008 km/min South.

Therefore, the girl's average velocity for her walk to school is -0.008 km/min South.