Question

one of these representations is not like the others. tap on the one that doesnt belong. arrows represent velocity vectors arrows represent acceleration vectors

Explanation:

Step1: Analyze the velocity - vector diagram

In projectile motion, the horizontal component of velocity \(v_x\) is constant (assuming no air - resistance), and the vertical component of velocity \(v_y\) changes linearly (because \(a_y=-g=- 9.8\ m/s^2\)). In the velocity - vector diagram (left - hand side upper diagram), the horizontal arrows (representing \(v_x\)) should be of the same length (constant \(v_x\)), and the vertical arrows (representing \(v_y\)) should change in length linearly.

Step2: Analyze the acceleration - vector diagram

In projectile motion, the acceleration is \(a = g\) (downward) throughout the motion. So, in the acceleration - vector diagram (right - hand side upper diagram), all the acceleration vectors (arrows) should be of the same length and direction (downward).

Step3: Analyze the \(d_x - d_y\) table

From the equations of motion: \(x = v_{0x}t\) (where \(v_{0x}\) is constant) and \(y=v_{0y}t-\frac{1}{2}gt^{2}\). If \(v_{0y} = 0\), \(x = v_{0x}t\) (linear relationship between \(x\) and \(t\): \(d_x=v_{0x}t\), and \(d_y=-\frac{1}{2}gt^{2}\)). The values in the \(d_x - d_y\) table are consistent with \(d_x = 8t\) (\(v_{0x}=8\ m/s\)) and \(d_y=-\frac{1}{2}(9.8)t^{2}\)

Step4: Analyze the \(v_x - v_y\) table

From the equations of motion: \(v_x=v_{0x}\) (constant) and \(v_y = v_{0y}-gt\). If \(v_{0x} = 12\ m/s\) and \(a=-g=-9.8\ m/s^{2}\), the values in the \(v_x - v_y\) table are consistent with \(v_x = 12\ m/s\) (constant) and \(v_y=0 - 9.8t\)

The odd - one - out is the velocity - vector diagram (left - hand side upper diagram). In a proper velocity - vector diagram for projectile motion (with \(v_{0y}
eq0\) initially), the horizontal components of velocity vectors (arrows) should be of the same length (constant \(v_x\)), but in the given velocity - vector diagram, the lengths of the horizontal arrows (supposed to represent \(v_x\)) do not seem to follow the rule of a constant \(v_x\) (if we assume a proper scale).

Answer:

The velocity - vector diagram (the left - hand side upper diagram)