Question

The height of a projectile launched upward at a speed of 80 feet/second from a heightof 384 feet is given by the function h(t) = - 16t^2+ 80t + 384. How long will it take theprojectile to hit the ground?

Answer 1

It will take the projectile 8 seconds to hit the ground

Here, we want to get the time it will take the projectile to hit the ground

To do this, we need to use the height on the ground. On the ground, the projectile has a height of 0

Thus, we have it that;

`\begin{gathered} 0=-16t^2+80t+384 \\ \text{divide through by }16 \\ 0=-t^2\text{ + 5t + 24} \\ -t^2\text{ + 5t + 24 = 0} \\ -t^2-3t\text{ + 8t + 24 = 0} \\ -t(t+3)+8(t+3)\text{ = 0} \\ (-t+8)(t+3)\text{ = 0} \\ -t\text{ + 8 = 0 or t +3 = 0} \\ t\text{ = 8 or -3} \end{gathered}`

Since time cannot be negative, we have the time as 8 seconds