Formula Free fall / Inclined plane Velocity Starting height Height
$$v ~=~ \sqrt{2g \, (h_0 ~-~ h)}$$ $$v ~=~ \sqrt{2g \, (h_0 ~-~ h)}$$ $$h_0 ~=~ h ~+~ \frac{ v^2 }{ 2g }$$ $$h ~=~ h_0 ~-~ \frac{ v^2 }{ 2g }$$ $$g ~=~ \frac{ v^2 }{ 2\,(h_0 - h) }$$
Velocity
$$ v $$ Unit $$ \frac{\mathrm m}{\mathrm s} $$ Current velocity of the falling body. The velocity of the body does not depend on whether the body is dropped straight down or e.g. glides down along an inclined plane (frictionless).
For example, a body is dropped from the starting height \(h_0 = 100 \, \text{m}\) above the ground (so the ground represents zero height). Thus, the velocity \(v\) of the body at height \(h = 10 \, \text{m} \) would be:\[ v ~=~ \sqrt{2g \, (100 \, \text{m} ~-~ 10 \, \text{m})} ~=~ 42 \, \frac{\text m}{\text s} \]
Starting height
$$ h_0 $$ Unit $$ \mathrm{m} $$ It is the height from which the body is dropped or glided on a plane.
Height
$$ h $$ Unit $$ \mathrm{m} $$ This is the current height at which the body is located.
Gravitational acceleration
$$ g $$ Unit $$ \frac{\mathrm{m}}{\mathrm{s}^2} $$ It is the acceleration - caused by the gravitational force - near the earth's surface. On the Earth it has the approximate value of \( g ~=~ 9.8 \, \frac{\text m}{\text{s}^2} \). On other planets (e.g. on Jupiter) this value is different.