Question

one of these representations is not like the others. tap on the one that doesnt belong.

Explanation:

Step1: Analyze the first graph

In the first graph, the arrows represent velocity vectors. In projectile motion, the horizontal component of velocity ($v_x$) remains constant (assuming no air - resistance), and the vertical component of velocity ($v_y$) changes due to gravity. The horizontal arrows (representing $v_x$) should be of the same length (constant magnitude), and the vertical arrows (representing $v_y$) should change in length.

Step2: Analyze the second graph

In the second graph, the arrows represent acceleration vectors. In projectile motion, the acceleration is constant and equal to the acceleration due to gravity ($g = 9.8\ m/s^{2}$) acting vertically downwards. There is no horizontal acceleration. So, all the acceleration vectors should be of the same length (constant magnitude) and directed vertically downwards. But in the second graph (the one with the red box), if we assume it's supposed to be similar to the first in terms of projectile - related vector representation (but mis - represented), it's incorrect.

Step3: Analyze the first table

The first table shows the horizontal distance ($d_x=v_{0x}t$, where $v_{0x} = 8\ m/s$ as $d_x$ at $t = 1\ s$ is $8\ m$, $t=2\ s$ is $16\ m$ etc.) and vertical distance ($d_y=v_{0y}t-\frac{1}{2}gt^{2}$, with $v_{0y} = 0$). This is consistent with projectile motion equations $d_x=v_{0x}t$ and $d_y=-\frac{1}{2}gt^{2}$ (taking downwards as negative).

Step4: Analyze the second table

The second table shows the horizontal velocity ($v_x$) is constant ($v_x=12\ m/s$) and the vertical velocity ($v_y = v_{0y}-gt$, with $v_{0y} = 0$) which is $v_y=-gt$ (since $g = 9.8\ m/s^{2}$, at $t = 1\ s$, $v_y=-9.8\ m/s$, at $t = 2\ s$, $v_y=- 19.6\ m/s$ etc.). This is also consistent with projectile motion equations $v_x = v_{0x}$ (constant) and $v_y=v_{0y}-gt$.

Answer:

The graph with the red box (the one where arrows represent acceleration vectors in a non - standard way for projectile motion as described above)