The acceleration of gravity on the moon is about 1.6 m/sec2. An experiment to test gravity compares the time it takes objects to reach a speed of 10 m/sec after being dropped from rest. How long does an object dropped on the moon have to fall compared to an object dropped on Earth?

a. 1.6 times as long
b. 6.1 times as long
c. 9.8 times as long
d. 15.7 times as long

The product of acceleration and time = 10 m/s.

1.6*t(moon) = 9.8* t(Earth)
t(moon)/t(Earth) = 9.8/1.6 = 6.1

To find out how long an object dropped on the moon takes to fall compared to an object dropped on Earth, we need to compare the initial acceleration due to gravity on each celestial body.

The acceleration due to gravity on the moon is about 1.6 m/sec^2, while on Earth it is approximately 9.8 m/sec^2.

Since the time taken for an object to reach a certain speed after being dropped from rest is dependent on its acceleration, we can calculate the ratio of the two times using the formula:

Time taken for object on the moon / Time taken for object on Earth = √(acceleration due to gravity on moon / acceleration due to gravity on Earth)

Let's substitute the values into the formula:

Time taken for object on the moon / Time taken for object on Earth = √(1.6 / 9.8)

Calculating this, we find:

Time taken for object on the moon / Time taken for object on Earth ≈ 0.354

Therefore, an object dropped on the moon takes roughly 0.354 times as long to fall compared to an object dropped on Earth.

Given the answer choices, the closest option is a. 1.6 times as long.

To compare the time it takes for an object to fall on the moon compared to the time it takes for an object to fall on Earth, we need to use the equation for the time it takes an object to fall a certain distance. The equation is:

t = √(2h / g)

Where:
t = time (in seconds)
h = height (in meters)
g = acceleration due to gravity (in m/s^2)

On the moon, the value of g is given as 1.6 m/s^2. We can assume the height is the same on both the moon and Earth for this comparison.

Let's assume the height is h = 10 m (since we are comparing the time it takes for the objects to reach a speed of 10 m/s).

For an object dropped on the moon:
t_moon = √(2 * 10 / 1.6) = √(12.5) = 3.54 seconds (approx.)

For an object dropped on Earth:
t_earth = √(2 * 10 / 9.8) = √(2.04) = 1.43 seconds (approx.)

Therefore, the object dropped on the moon takes approximately 3.54 seconds to fall compared to the object dropped on Earth, which takes approximately 1.43 seconds to fall.

Since 3.54 seconds is approximately 2.47 times longer than 1.43 seconds, the correct answer is not provided in the options given.