`h=-16t^(2) + vt + k`
The equation above gives the height h, in feet, of a ball t seconds after it is thrown straight up with an initial speed of v feet per second from a height of k feet. Which of the following gives v in terms of h, t, and k ?

Options

A. `v=h + k - 16t`
B. `v=(h-k + 16)/t`
C. `v=(h+k)/t - 16t`
D. `v=(h-k)/t + 16t`

Answer

To solve for \( v \) in terms of \( h \), \( t \), and \( k \) from the equation \( h = -16t^2 + vt + k \), we can follow these steps:

### Step 1: Write down the original equation
We start with the given equation:
\[ h = -16t^2 + vt + k \]

### Step 2: Rearrange the equation to isolate \( vt \)
To isolate \( vt \), we can move \( -16t^2 \) and \( k \) to the left side:
\[ vt = h + 16t^2 - k \]

### Step 3: Solve for \( v \)
Now, we can solve for \( v \) by dividing both sides by \( t \):
\[ v = \frac{h + 16t^2 - k}{t} \]

### Step 4: Simplify the expression
We can simplify the expression further:
\[ v = \frac{h - k}{t} + 16t \]

### Final Expression
Thus, the final expression for \( v \) in terms of \( h \), \( t \), and \( k \) is:
\[ v = \frac{h - k}{t} + 16t \]