Question

analyzing projectile motion
which statements are true regarding the data represented by the scatter - plot 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 function - shape relationships

Exponential functions have a characteristic rapid - growth or decay curve. Linear functions have a constant rate of change and form a straight line. Quadratic functions have a parabolic shape.

Step2: Analyze the scatter - plot

The scatter - plot of projectile motion has a parabolic shape. The height of a projectile follows a quadratic relationship because the equation for the height \(h(t)\) of a projectile under the influence of gravity is \(h(t)=- \frac{1}{2}gt^{2}+v_{0}t + h_{0}\), where \(g\) is the acceleration due to gravity, \(v_{0}\) is the initial velocity, and \(h_{0}\) is the initial height. Also, the rate of change of height (velocity) is not constant as the projectile is affected by gravity.

Answer:

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