Question

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?

Answer 1

`t = 1.94` `"s"`

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"" ")|)`