when apollo 15 astronaut David Scott dropped a hammer and a feather on the moon to demostrate that in a vacuum all bodies fall with the same (constant) acceleration, he droppes them from 4 feet above the lunar surface. the television shows them fallen more slowly than on earth, where ina vacum it would take only half a second for the fall of 4 feet. how long did it take the hammer and the feather to fall 4 feet ont he moon, if the moons gravitational acceleration is 13/80 that of earth?
H = (1/2) a t^2
t = sqrt(2H/a)
H is the height, which is kept constant. Since acceleration (a) is decreased by a factor 13/80, the time to fall is increased by a factor
sqrt(80/13) = 2.48
On the moon, the time to fall 4 ft is given by the equation
4 ft = (1/2)* (13/80)*32.2 ft/s^2 * t^2
t = 1.24 s
To determine how long it took the hammer and the feather to fall 4 feet on the moon, we can use the equation for distance traveled (d) by an object falling under constant acceleration:
d = (1/2) * g * t^2
Where:
d = distance traveled (4 feet)
g = acceleration due to gravity (13/80 times that of Earth's)
t = time taken to fall
Substituting the given values, we have:
4 = (1/2) * (13/80) * t^2
To solve for t, we can rearrange the equation:
t^2 = (4 * 2) / ((13/80))
t^2 = (8) / (13/80)
Now, divide 8 by (13/80):
t^2 = 8 * (80/13)
t^2 = 640/13
Taking the square root of both sides:
t = sqrt( 640/13 )
Using a calculator, we find:
t ≈ 5.028 seconds
So, it took approximately 5.028 seconds for both the hammer and the feather to fall 4 feet on the moon.
To calculate the time it took for the hammer and the feather to fall 4 feet on the moon, we need to use the equation of motion:
Distance = (1/2) * acceleration * time^2
Since the distance is given as 4 feet and the acceleration on the moon is 13/80 times that of Earth, we can substitute the values into the equation:
4 = (1/2) * (13/80) * time^2
To solve for time, we need to isolate it. Let's simplify the equation first:
4 = (13/160) * time^2
Now, we can multiply both sides by 160 to get rid of the fraction:
160 * 4 = 13 * time^2
640 = 13 * time^2
Next, divide both sides by 13:
640/13 = time^2
Simplify the left side:
49.23 = time^2
Finally, take the square root of both sides to solve for time:
time = √49.23 ≈ 7 seconds
Therefore, it took approximately 7 seconds for both the hammer and the feather to fall 4 feet on the moon.