This graph shows the uniformly accelerated motion of a ball in free fall on another planet, with time $t$ on the x-axis (in seconds) and height $h$ of the ball on the y-axis (in meters). The graph displays a parabolic shape, which suggests that the ball's height decreases as it falls under the influence of gravity, following the equation for motion under constant acceleration:

$h(t) = h_0 - \frac{1}{2} g t^2$

where $h_0$ is the initial height, $g$ is the acceleration due to gravity, and $t$ is time.

Steps to find acceleration due to gravity ($g$):

1. The graph shows that the initial height of the ball is about 4.9 m when $t = 0$.
2. The ball reaches the ground (height $h = 0$) at around $t = 0.5$ seconds.
3. Using the kinematic equation for uniformly accelerated motion:

$h(t) = h_0 - \frac{1}{2} g t^2$

Set $h(t) = 0$ when the ball reaches the ground, and substitute $h_0 = 4.9 \, \text{m}$ and $t = 0.5 \, \text{s}$:

$0 = 4.9 - \frac{1}{2} g (0.5)^2$

Now solve for $g$:

$4.9 = \frac{1}{2} g \times 0.25$ $4.9 = 0.125 g$ $g = \frac{4.9}{0.125} = 39.2 \, \text{m/s}^2$

Thus, the acceleration due to gravity on this planet is approximately $39.2 \, \text{m/s}^2$.

Would you like further details on any part of this explanation?

Here are some related questions:

1. How is free fall motion described mathematically?
2. How would the graph look if the acceleration due to gravity were lower?
3. What other kinematic equations can describe free-fall motion?
4. How does gravity vary on different planets?
5. What experiments can be done to measure gravity in a similar setup?

Tip: In free-fall problems, the initial velocity is typically zero when an object is dropped from rest.