Calculate the time required for an astronaut to
free-fall 50 m on the Moon.
Please show and explain steps answer is 7.9s
g = 9.8/6 = 1.633333 m/s^2 on moon.
d = o.5g*t^2 = 50 m.
0.5*1.63333*t^2 = 50
0.81666t^2 = 50
t^2 = 61.22
t = 7.82 s.
To calculate the time required for an astronaut to free-fall 50 m on the Moon, we can use the formula for free-fall time:
t = sqrt(2h/g)
Where:
t is the time in seconds,
h is the height in meters, and
g is the acceleration due to gravity in m/s^2.
1. Determine the acceleration due to gravity on the Moon.
The acceleration due to gravity on the Moon is approximately 1/6th of the acceleration due to gravity on Earth, which is approximately 9.8 m/s^2. Therefore, the acceleration due to gravity on the Moon is determined by dividing 9.8 m/s^2 by 6:
g = 9.8 m/s^2 / 6 ≈ 1.63 m/s^2
2. Substitute the values into the formula:
t = sqrt(2h/g)
t = sqrt(2 * 50 m / 1.63 m/s^2)
t = sqrt(100 m / 1.63 m/s^2)
t = sqrt(61.35 s^2/m)
t ≈ 7.83 s
Therefore, it would take approximately 7.83 seconds (rounded to one decimal place or 7.9s) for an astronaut to free-fall 50 meters on the Moon.