Question

fill in the blank question the picture shows a yellow ball (on the left) that was released from rest at the same time that a red ball (on the right) was given an initial horizontal velocity. the picture shows their simultaneous positions at various instants. despite their different paths, the red and yellow balls are at the same height at any given instant. this is because both balls have the same

Explanation:

Step1: Analyze vertical motion

Vertical - motion of both balls is free - fall. The equation for vertical displacement is $y = y_0+v_{0y}t-\frac{1}{2}gt^{2}$, where for both balls $v_{0y} = 0$ (yellow starts from rest vertically and red has no initial vertical velocity), $y_0$ is the initial height, and $g$ is the acceleration due to gravity.

Step2: Consider time and acceleration

Since the acceleration due to gravity $g$ is the same for both balls and the initial vertical conditions are equivalent (same initial height and zero initial vertical velocity for both in the relevant sense), they will have the same vertical displacement at any given time.

Answer:

vertical acceleration