Question

on a mysterious orb in a distant galaxy, some alien creatures conduct an experiment to verify the value of \g\ on their planet. they drop a rock from the ceiling 2.7 meters high and record the time it takes to hit the ground to be 0.61 seconds. find the value of \g\

Explanation:

Step1: Identify the kinematic - equation

The kinematic equation for free - fall is $h = v_0t+\frac{1}{2}gt^2$. Since the rock is dropped ($v_0 = 0$), the equation simplifies to $h=\frac{1}{2}gt^2$.

Step2: Rearrange the equation to solve for g

We can rewrite $h=\frac{1}{2}gt^2$ as $g=\frac{2h}{t^2}$.

Step3: Substitute the given values

Given $h = 2.7$ meters and $t = 0.61$ seconds. Substitute these values into the formula: $g=\frac{2\times2.7}{(0.61)^2}$.

Step4: Calculate the value of g

First, calculate the numerator: $2\times2.7 = 5.4$. Then, calculate the denominator: $(0.61)^2=0.3721$. So, $g=\frac{5.4}{0.3721}\approx14.5$ m/s².

Answer:

14.5 m/s/s