Question

a penny is dropped from a window. which graph could represent the height of the penny, in feet, as a function of time in seconds?

Explanation:

Step1: Analyze the motion of the penny

When a penny is dropped from a window, it falls downwards under the influence of gravity. Its height above the ground decreases over time. The motion is a non - linear one because the speed of the penny increases as it falls (due to acceleration due to gravity $g\approx 32\mathrm{ft/s}^2$), following the equation $h = h_0-\frac{1}{2}gt^2$ (where $h_0$ is the initial height, $g$ is the acceleration due to gravity and $t$ is time).

Step2: Evaluate each graph

• Graph A shows the height increasing with time, which is incorrect as the penny is falling.
• Graph B shows a linear decrease in height. But the motion of a falling object is not linear (it is quadratic due to the acceleration), so this is incorrect.
• Graph C shows the height increasing initially which is wrong for a falling object.
• Graph D shows a non - linear decrease in height, which is consistent with the motion of an object falling under the influence of gravity.

Answer:

D.