Question

describe and correct the error a student made when interpreting the graph of the vertical motion model ( h(t) = at^2 + bt + c ).
click the icon to view the students interpretation.
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. in a graph of a vertical motion model, the x - axis represents time, not horizontal distance.
b. the object reaches its maximum height at a distance of (square) feet, not 4 feet.
c. the horizontal motion model is measured in units of meters, not feet.
d. the maximum height of the object cannot be determined from the graph.

interpretation
the object reaches its maximum height after traveling a distance of 4 feet horizontally.

Explanation:

The student misinterpreted the x - axis of the vertical motion model graph. In a vertical motion model \( h(t)=at^{2}+bt + c \), the x - axis represents time (the independent variable, which is the time elapsed since the object started its vertical motion), not the horizontal distance traveled by the object. Option A correctly identifies this error as it states that in the graph of the vertical motion model, the x - axis represents time, not horizontal distance. Option B is incorrect because the issue is about the meaning of the x - axis (time vs. horizontal distance), not the units of the maximum height's horizontal component. Option C is incorrect as the problem is not about the units of the horizontal motion model but the misinterpretation of the x - axis in the vertical motion model. Option D is incorrect as the maximum height can be determined from the y - value of the vertex of the parabola (the graph of the vertical motion model is a parabola), so we can find the maximum height from the graph.

Answer:

A. In a graph of a vertical motion model, the x - axis represents time, not horizontal distance.