Question: The height of a projectile, in feet, is given by the formula $h(t) = -16t^2 + 128t + 5$, where $t$ represents time in seconds. Find the initial height of the projectile.
1. **State the problem:** We need to find the initial height of the projectile given by the height function $$h(t) = -16t^2 + 128t + 5$$ where $t$ is time in seconds.
2. **Understand the initial height:** The initial height is the height of the projectile at time $t=0$ seconds.
3. **Calculate the initial height:** Substitute $t=0$ into the height formula:
$$h(0) = -16(0)^2 + 128(0) + 5$$
4. **Simplify the expression:**
$$h(0) = 0 + 0 + 5 = 5$$
5. **Interpretation:** The initial height of the projectile is $5$ feet.
**Final answer:** The initial height was $5$ ft.