Solve for v0 h(t)=-16t^2+v_0t+h_0

$h (t) = - 16 t^{2} + v_{0} t + h_{0}$

Step 1

Divide each term in $h t = - 16 t^{2} + v_{0} t + h_{0}$ by $t$ .

$\frac{h t}{t} = \frac{- 16 t^{2}}{t} + \frac{v_{0} t}{t} + \frac{h_{0}}{t}$

Step 2

Simplify the left side.

Cancel the common factor of $t$ .

Cancel the common factor.

$\frac{h t}{t} = \frac{- 16 t^{2}}{t} + \frac{v_{0} t}{t} + \frac{h_{0}}{t}$

Divide $h$ by $1$ .

$h = \frac{- 16 t^{2}}{t} + \frac{v_{0} t}{t} + \frac{h_{0}}{t}$

Step 3

Simplify the right side.

Simplify each term.

Cancel the common factor of $t^{2}$ and $t$ .

Factor $t$ out of $- 16 t^{2}$ .

$h = \frac{t (- 16 t)}{t} + \frac{v_{0} t}{t} + \frac{h_{0}}{t}$

Cancel the common factors.

Raise $t$ to the power of $1$ .

$h = \frac{t (- 16 t)}{t^{1}} + \frac{v_{0} t}{t} + \frac{h_{0}}{t}$

Factor $t$ out of $t^{1}$ .

$h = \frac{t (- 16 t)}{t \cdot 1} + \frac{v_{0} t}{t} + \frac{h_{0}}{t}$

Cancel the common factor.

$h = \frac{t (- 16 t)}{t \cdot 1} + \frac{v_{0} t}{t} + \frac{h_{0}}{t}$

Rewrite the expression.

$h = \frac{- 16 t}{1} + \frac{v_{0} t}{t} + \frac{h_{0}}{t}$

Divide $- 16 t$ by $1$ .

$h = - 16 t + \frac{v_{0} t}{t} + \frac{h_{0}}{t}$

Cancel the common factor of $t$ .

Cancel the common factor.

$h = - 16 t + \frac{v_{0} t}{t} + \frac{h_{0}}{t}$

Divide $v_{0}$ by $1$ .

$h = - 16 t + v_{0} + \frac{h_{0}}{t}$