Question

which statements are true regarding the data represented by the scatterplot of projectile motion? check all that apply. the data shows an exponential relationship. the data shows a quadratic relationship. the data shows a linear relationship. the height will increase over time at a constant rate of change. the change in height compared to the change in time is not constant.

Explanation:

Step1: Recall motion equations

Projectile - motion height \(h(t)\) is given by \(h(t)=- \frac{1}{2}gt^{2}+v_{0}t + h_{0}\), which is a quadratic function (\(g\) is acceleration due to gravity, \(v_{0}\) is initial velocity, \(h_{0}\) is initial height).

Step2: Analyze rate of change

The rate of change of a quadratic function \(y = ax^{2}+bx + c\) is not constant. The slope of the tangent line to the graph of a quadratic function changes as \(x\) changes.

Answer:

The data shows a quadratic relationship.
The change in height compared to the change in time is not constant.