An object is released from rest on a planet
that has no atmosphere. The object falls
freely for 2.73 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 equations of motion for free fall.
The equation we'll use is:
d = (1/2) * g * t^2
Where:
d = distance fallen (2.73 m)
g = acceleration due to gravity (unknown)
t = time (1 second)
Plugging in the values:
2.73 = (1/2) * g * (1)^2
To find g, we'll rearrange the equation:
2.73 = (1/2) * g
Multiply both sides by 2:
2.73 * 2 = g
g = 5.46 m/s^2
Therefore, the magnitude of the acceleration due to gravity on the planet is 5.46 m/s^2.
To find the magnitude of the acceleration due to gravity on the planet, we can use the formula for free fall:
d = (1/2) * g * t^2
where:
d = distance fallen (2.73 m)
g = acceleration due to gravity on the planet (what we need to find)
t = time (1 second)
Rearranging the formula, we get:
g = (2 * d) / t^2
Substituting the given values:
g = (2 * 2.73 m) / (1 second)^2
Simplifying the equation, we get:
g = 2 * 2.73 m/s^2
Therefore, the magnitude of the acceleration due to gravity on the planet is 5.46 m/s^2.
s = 1/2 at^2
2.73 = a/2
a = 5.46m/s^2