Question

What is the terminal velocity of an object which has been dropped after it has fallen 10 meters?

Answer 1

`10sqrt(2)` meters/second

Explanation:

Acceleration due to gravity `= 9.8 "meters"/("second")^2`
However, because I'm lazy, I will assume that it is close enough to `10 "meters"/("second")^2` to not make any significant difference.

Assuming an initial velocity of `0`

Distance traveled can be computed as
`color(white)("XXXX")` `d = 1/2at^2` where `a` is the accelration and `t` is the time.

We are told the distance is 10 meters and using `a = 10 "m"/(s"^2)`

`color(white)("XXXX")` `10 m = 1/2 * 10 m/sec^2* t^2 sec`
`color(white)("XXXX")` `rArr t^2 = 2 " sec"`
`color(white)("XXXX")` `rArr t =sqrt(2) sec.`

With an initial velocity of `0` and an acceleration of `10 m/(s^2)`
the terminal velocity after `sqrt(2)` sec. will be `10 sqrt(2)` m/sec