To find the acceleration due to gravity $g$ on the unknown planet, we can use the kinematic equation for free fall:

$d = \frac{1}{2} g t^2$

Where:

• $d$ is the distance the wrench falls (3.00 m),
• $t$ is the time it takes to fall (0.814 s),
• $g$ is the acceleration due to gravity (which we need to find).

Rearranging the equation to solve for $g$:

$g = \frac{2d}{t^2}$

Now, substitute the given values:

$g = \frac{2 \times 3.00 \, \text{m}}{(0.814 \, \text{s})^2}$

Let's calculate this.The acceleration due to gravity on this unknown planet is approximately $9.06 \, \text{m/s}^2$.

Would you like further details or have any questions?

Here are 5 related questions:

1. How does this acceleration compare to Earth's gravitational acceleration?
2. How would you calculate the time it takes for the wrench to fall if you knew the gravity of the planet beforehand?
3. What other factors might affect the fall of the wrench besides gravity?
4. How would the result change if air resistance were significant?
5. Can you determine the mass of the planet using only the gravitational acceleration and the planet's radius?

Tip: When analyzing free fall, always remember to exclude factors like air resistance unless specified.