Wa projectle is fred straight upward from the ground with an initial speed of 160 feet per second, then its height h in feet after I seconds is given by the function h(t)=-16t^2+160t Find the maximum height of the projectile

To find the maximum height of the projectile, we need to find the vertex of the parabolic function $h(t)=-16t^{2}+160t$. The vertex of a parabola in the form $f(t)=at^{2}+bt+c$ is given by the formula $t=-\frac{b}{2a}$.<br /><br />In this case, $a=-16$ and $b=160$. Plugging these values into the formula, we get:<br /><br />$t=-\frac{160}{2(-16)}$<br /><br />Simplifying, we have:<br /><br />$t=-\frac{160}{-32}$<br /><br />$t=5$<br /><br />So, the maximum height occurs at $t=5$ seconds.<br /><br />To find the maximum height, we substitute $t=5$ into the function $h(t)$:<br /><br />$h(5)=-16(5)^{2}+160(5)$<br /><br />Simplifying, we have:<br /><br />$h(5)=-16(25)+800$<br /><br />$h(5)=-400+800$<br /><br />$h(5)=400$<br /><br />Therefore, the maximum height of the projectile is 400 feet.