Question

a soccer ball is kicked from the ground with an initial upward velocity of 90 feet per second. the equation h(t)=-16t² + 90t gives the height h of the ball in t seconds. how many seconds will it take for the ball to reach its maximum height? (round to the nearest hundredth.)

Explanation:

Step1: Identify the formula for time at maximum height

For a quadratic function \(h(t)= - 16t^{2}+v_{0}t + h_{0}\) (in this case \(h_{0} = 0\)), the time \(t\) at which the maximum height is reached is given by the formula \(t=-\frac{b}{2a}\) from the quadratic form \(y = ax^{2}+bx + c\). Here, \(a=-16\) and \(b = 90\).

Step2: Calculate the time

Substitute \(a=-16\) and \(b = 90\) into the formula \(t =-\frac{b}{2a}\).

$$ t=-\frac{90}{2\times(-16)}=\frac{90}{32}=2.8125\approx2.81 $$

Answer:

\(2.81\)