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?
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.