To find the acceleration due to gravity on the planet, we can use the kinematic equation that relates initial velocity, maximum height, and acceleration:

$v^2 = u^2 + 2a s$

Where:

• $v$ is the final velocity (0 m/s at the maximum height),
• $u$ is the initial velocity (6.0 m/s),
• $a$ is the acceleration due to gravity (negative because it opposes the motion),
• $s$ is the maximum height (27 m).

We can rearrange this equation to solve for $a$:

$0 = (6.0)^2 + 2 \cdot a \cdot (27)$

Now, let's solve for $a$.

$0 = 36 + 54a$ $54a = -36$ $a = \frac{-36}{54} = -\frac{2}{3} \, \text{m/s}^2$

So, the magnitude of the acceleration due to gravity on the planet is:

$\boxed{0.67 \, \text{m/s}^2}$

Would you like more details or have any questions?

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Here are some related questions to explore:

1. How does gravity on Earth compare to gravity on this planet?
2. What would be the time of flight for the astronaut’s jump?
3. How much energy does the astronaut use to jump to a height of 27 m?
4. How would air resistance affect the astronaut's jump if there was an atmosphere?
5. How would the astronaut's weight differ on this planet compared to Earth?

Tip: When using kinematic equations, always double-check units and signs, especially for acceleration.