Can't unless we define v = dh/dt to be the vertical speed.
In which case, dh/dt = v = v0 - gt ANS.
Steve is correct if you really wanted v0 = ?, but that's not what you asked for.
I guess you mean solve for v₀.
Well, here's one way, with all the steps.
h = h₀ + v₀t ‐½gt²
Add ½gt² to both sides
h + ½gt² = h₀ + v₀t ‐½gt² + ½gt²
h + ½gt² = h₀ + v₀t
Subtract h₀ from both sides
h - h₀ + ½gt² = h₀ + v₀t - h₀
h - h₀ + ½gt² = v₀t
Divide both sides by t
(h - h₀ + ½gt²)/t = v₀t / t
(h - h₀ + ½gt²)/t = v₀
Rewrite with v₀ on the left:
v₀ = (h - h₀ + ½gt²)/t
Simplify a bit if required
v₀ = (h - h₀)/t + (½gt²))/t
= (h - h₀)/t + ½gt
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Can't unless we define v = dh/dt to be the vertical speed.
In which case, dh/dt = v = v0 - gt ANS.
Steve is correct if you really wanted v0 = ?, but that's not what you asked for.
I guess you mean solve for v₀.
Well, here's one way, with all the steps.
h = h₀ + v₀t ‐½gt²
Add ½gt² to both sides
h + ½gt² = h₀ + v₀t ‐½gt² + ½gt²
h + ½gt² = h₀ + v₀t
Subtract h₀ from both sides
h - h₀ + ½gt² = h₀ + v₀t - h₀
h - h₀ + ½gt² = v₀t
Divide both sides by t
(h - h₀ + ½gt²)/t = v₀t / t
(h - h₀ + ½gt²)/t = v₀
Rewrite with v₀ on the left:
v₀ = (h - h₀ + ½gt²)/t
Simplify a bit if required
v₀ = (h - h₀)/t + (½gt²))/t
= (h - h₀)/t + ½gt