Question

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. How long will it take for the projectile go hit it’s target on the ground?

Answer 1

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

`\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}`

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