The problem involves the concept of acceleration due to gravity. On the moon, the acceleration due to gravity is about 1/6th of that on Earth, or approximately 1.6 m/s². However, the problem states that the marble falls 4.00 m in the first second. This suggests that the acceleration due to gravity in this scenario is actually 4.00 m/s², not 1.6 m/s².

The distance an object falls under constant acceleration is given by the equation d = 0.5*a*t², where d is the distance, a is the acceleration, and t is the time.

In the first second (t = 1.0 s), the marble falls 4.00 m. We can use this information to solve for the acceleration:

4.00 m = 0.5*a*(1.0 s)²
4.00 m = 0.5*a*1.0 m/s²
4.00 m = 0.5*a
a = 4.00 m / 0.5 = 8.00 m/s²

So the acceleration due to gravity in this scenario is 8.00 m/s².

In the next second (from t = 1.0 s to t = 2.0 s), we want to find the additional distance the marble falls. We can use the same equation, but we need to subtract the distance the marble has already fallen:

d = 0.5*a*t² - d_already_fallen
d = 0.5*8.00 m/s²*(2.0 s)² - 4.00 m
d = 0.5*8.00 m/s²*4.00 s² - 4.00 m
d = 16.00 m - 4.00 m
d = 12.00 m

So the marble falls an additional 12.00 m in the next second.

Question

The problem involves the concept of acceleration due to gravity. On the moon, the acceleration due to gravity is about 1/6th of that on Earth, or approximately 1.6 m/s². However, the problem states that the marble falls 4.00 m in the first second. This suggests that the acceleration due to gravity in this scenario is actually 4.00 m/s², not 1.6 m/s².

The distance an object falls under constant acceleration is given by the equation d = 0.5*a*t², where d is the distance, a is the acceleration, and t is the time.

In the first second (t = 1.0 s), the marble falls 4.00 m. We can use this information to solve for the acceleration:

4.00 m = 0.5*a*(1.0 s)²
4.00 m = 0.5*a*1.0 m/s²
4.00 m = 0.5*a
a = 4.00 m / 0.5 = 8.00 m/s²

So the acceleration due to gravity in this scenario is 8.00 m/s².

In the next second (from t = 1.0 s to t = 2.0 s), we want to find the additional distance the marble falls. We can use the same equation, but we need to subtract the distance the marble has already fallen:

d = 0.5*a*t² - d_already_fallen
d = 0.5*8.00 m/s²*(2.0 s)² - 4.00 m
d = 0.5*8.00 m/s²*4.00 s² - 4.00 m
d = 16.00 m - 4.00 m
d = 12.00 m

So the marble falls an additional 12.00 m in the next second.

Knowee AI · Accepted Answer