The projectile hits the target after 2.5 seconds.
Solution:
Given, A trebuchet launches a projectile from ground level on a parabolic arc at a velocity of 40 feet per second.
The equation h = -16t^2+40t models the projectiles height at t seconds.
We have to find how long will it take for the projectile go hit it’s target on the ground?
Now, when the projectile hits its target on ground, its height becomes 0
[tex]\begin{array}{l}{\text { So, } 0=-16 t^{2}+40 t} \\\\ {\rightarrow t(-16 t+40)=0} \\\\ {\rightarrow t=0 \text { or }-16 t+40=0}\end{array}[/tex]
neglect t = 0 as it represents initial phase of projectile.
16t = 40
t = 2.5
Hence, the projectile hits the target after 2.5 seconds
