Alien home world physics

Question

You are abducted by aliens who transport you to their home world in a galaxy far far away. Oddly the only thing you can think about is measuring the acceleration due to gravity on the strange new world. You drop an alien paperweight from a height of 12m and use an alien stopwatch to measure the interval of 1.36s it takes the paperweight to hit the ground below. What is the acceleration due to gravity on the alien home world?

Answer 1

Using the kinematic equation of motion:

x_f = x_i + v_it + ½ at²

where x_i = 0 and v_i = 0 (because you can start your frame of reference from where the object is dropped and the object is indeed just dropped so it starts with zero velocity)

So, that reduces the equation to:

x_f = ½ at² or solving for acceleration, a = 2x_f/t²

x_f = -12m because you drop the object and it ends up 12m below you and t = 1.36s so:

a = 2(-12)/1.36² = -12.976 m/s². Since the givens have at most 2 significant figures, we round the answer to -13 m/s² (note that the negative sign just means that the acceleration due to gravity is down)