Question

emily lives in a third - floor apartment. this morning, she walks downstairs to go to school. when she reaches the bottom of the stairs, she realizes that she forgot her spanish book! she rushes upstairs, quickly grabs the book, and then races back down again. which graph could show emily’s height above the ground over time? two graphs are shown with y - axis labeled height above ground (ft.) and x - axis labeled time (min.)

Explanation:

Step1: Analyze Initial Height

Emily starts at the third - floor, so her initial height above the ground is non - zero. The left graph starts with a non - zero \(y\) - value (height), while the right graph starts at \(y = 0\).

Step2: Analyze Motion Phases

• First, she walks downstairs: her height above the ground should decrease over time until she reaches the bottom (height = 0).
• Then, she rushes upstairs: her height should increase back to the third - floor height.
• Then, she grabs the book (a short time where height is constant) and then races back down: her height decreases again to 0. The left graph shows a decrease (downstairs), then an increase (upstairs) to the original height, a short constant (grabbing the book), and then a decrease (racing down). The right graph starts at 0, which is incorrect as Emily starts at the third - floor.

Answer:

The graph on the Left