After landing on an unfamiliar planet, a space explorer constructs a simple pendulum of length 55.0 cmcm. She finds that the pendulum makes 110 complete swings in a time of 145 ss.

First, let's find the period of the pendulum. This can be found by solving for the amount of time it takes for the pendulum to make ONE complete swing.

[tex]T = \frac{\text{Total time}}{\text{Number of complete swings} }\\\\T = \frac{145}{110} = 1.318 s[/tex]

Now, let's use the equation for the period of a simple pendulum:
[tex]T = 2\pi \sqrt{\frac{L}{g}}[/tex]

T = Period (1.318 s)
L = length of string (0.55 m)

g = acceleration due to gravity on planet (? m/s²)

Let's solve for 'g' doing some quick rearranging of the equation:
[tex]T^2 = 4 \pi^2 (\frac{L}{g})\\\\g = \frac{4\pi^2 L}{T^2}\\\\[/tex]

Solving for 'g' by plugging in values:
[tex]g = \frac{4\pi^2 (0.55)}{(1.318)^2}\\ \\= \boxed{12.496 \frac{m}{s^2}}[/tex]