Question

one of these representations is not like the others. tap on the one that doesnt belong. the time to rise to the peak location equals the time to fall from the peak location.

Explanation:

Step1: Analyze projectile motion properties

In projectile motion, the horizontal velocity \(v_x\) is constant (assuming no air - resistance), and the vertical acceleration \(a_y=-g=- 9.8\ m/s^{2}\) (constant). The time to rise to the peak \(t_{rise}=\frac{v_{0y}}{g}\) and the time to fall \(t_{fall}=\frac{v_{y}}{g}\) (where \(v_{y}\) has the same magnitude as \(v_{0y}\) at the same height).
The first graph (velocity vectors) shows constant \(v_x\) (horizontal component of velocity vectors are the same length) and changing \(v_y\) (vertical component of velocity vectors change). The table also shows constant \(v_x = 33.9\ m/s\) and \(v_y\) changing with \(a_y=\frac{\Delta v_y}{\Delta t}=\frac{9.8 - 19.6}{1}=-9.8\ m/s^{2}\) (constant acceleration). The statement “The time to rise to the peak location equals the time to fall from the peak location” is a property of projectile motion.

Step2: Analyze the acceleration - vector graph

In projectile motion, the acceleration is constant (\(a=-g\hat{j}\)). But in the acceleration - vector graph (the one with “Arrows Represent Acceleration Vectors”), if we assume projectile motion, the acceleration vectors should all be the same (magnitude and direction). However, looking at the lengths of the vertical vectors (since \(a = g\) is constant in projectile - motion, the acceleration vectors in \(y\) - direction should have the same length). If we assume standard projectile - motion (no air - resistance), the acceleration is \(a=-g\hat{j}\) (constant). The fact that the lengths of the “acceleration” vectors in the “Arrows Represent Acceleration Vectors” graph (the one in the bottom - right) seem to change (if we assume it's related to projectile - motion acceleration) is wrong. Because in projectile motion \(a = g\) (constant magnitude, downward direction)

Answer:

The one with “Arrows Represent Acceleration Vectors” (the graph in the bottom - right)