Final answer:
The magnitude of the acceleration due to gravity on the planet is calculated using the kinematic equation for uniform acceleration. With the given information, the acceleration is found to be 6.12 m/s².
Step-by-step explanation:
To calculate the magnitude of the acceleration due to gravity on a planet where an object falls freely for 3.06 meters in the first second, we can use the kinematic equation for uniformly accelerated motion:
s = ut + ½at²
Where:
- s is the distance the object falls (3.06 m),
- u is the initial velocity (0 m/s, since the object is released from rest),
- t is the time the object falls for (1 second),
- a is the acceleration due to gravity (what we want to find).
Plugging the values we have into the equation:
3.06 m = (0 m/s)(1 s) + ½(a)(1 s)²
3.06 m = ½a
Now we solve for a:
a = 2 × 3.06 m/s²
a = 6.12 m/s²
Therefore, the magnitude of the acceleration due to gravity on this planet is 6.12 m/s², which corresponds to option (a).