I am on the moon where gravity is 1.6 m/s/s downward. If I dropped a brick from a height of 3 m, how long did it take to hit the surface?
1 Answer
Explanation:
We're asked to find the time it takes an object to hit the ground, given its height and downward acceleration.
To do this, we can use the equation
#y = y_0 + v_(0y)t  1/2g t^2#
where

#y# is the final height (#0# , ground level) 
#y_0# is the initial height (given as#3# #"m"# ) 
#v_(0y)# is the initial#y# velocity (#0# since it was dropped from a state of rest) 
#t# is the time (what we're trying to find) 
#g# is the acceleration due to gravity (given as#1.6# #"m/s"^2# )
Plugging in known values, we have
#0 = 3color(white)(l)"m" + (0)t  1/2(1.6color(white)(l)"m/s"^2)t^2#
#(0.8color(white)(l)"m/s"^2)t^2 = 3color(white)(l)"m"#
#t = sqrt((3color(white)(l)"m")/(0.8color(white)(l)"m/s"^2)) = color(red)(ulbar(stackrel(" ")(" "1.94color(white)(l)"s"" "))#