An ob ject is released from rest on a planet
that has no atmosphere. The ob ject falls
freely for 5.04 m in the first second. What is the magnitude of the acceleration due to gravity on the planet?
To find the magnitude of the acceleration due to gravity on the planet, we can use the equation of motion for free fall:
s = ut + (1/2)at²
where:
s = displacement (in this case, 5.04 m)
u = initial velocity (since the object is released from rest, u = 0)
t = time (in this case, 1 second)
a = acceleration due to gravity (what we want to find)
We can rearrange the equation to solve for acceleration (a):
a = 2s / t²
Now, let's substitute the given values into the equation:
a = 2 * 5.04 m / (1 s)²
Simplifying further, we have:
a = 2 * 5.04 m / 1 s²
a = 10.08 m / 1 s²
a = 10.08 m/s²
Therefore, the magnitude of the acceleration due to gravity on the planet is 10.08 m/s².