An astronaut drops a hammer from 2.0 meters above the surface of the Moon. If the acceleration due to gravity on the Moon is 1.62 meters per second2, how long will it take for the hammer to fall to the Moon's surface?
To solve this problem, we can use the kinematic equation:
s = ut + (1/2)at²
Where:
s = displacement (in this case, the distance the hammer falls, which is 2.0 meters)
u = initial velocity (which is 0 as the hammer is dropped)
t = time
a = acceleration due to gravity on the Moon (1.62 meters per second²)
Plugging in the values, we have:
2.0 = 0( t) + (1/2)(1.62)(t²)
Simplifying the equation, we get:
2.0 = 0 + 0.81t²
Dividing both sides by 0.81, we have:
t² = 2.0 / 0.81
t² = 2.469
Taking the square root of both sides, we have:
t = √2.469
t ≈ 1.57 seconds
Therefore, it will take approximately 1.57 seconds for the hammer to fall to the Moon's surface.