Question

numeric 1 point
a soccer ball is kicked from the ground with an initial upward velocity of 90 feet per second. the equation ( h ( t ) = - 16 t ^ { 2 } + 90 t ) gives the height ( h ) of the ball in ( t ) seconds.
how long will it take the ball to reach the ground after being kicked? (round to the nearest hundredth.)
answer
previous

Explanation:

Step1: Set up the equation

When the ball reaches the ground, \(h(t)=0\). So we set \(-16t^{2}+90t = 0\).

Step2: Factor the equation

Factor out \(t\): \(t(-16t + 90)=0\).

Step3: Solve for \(t\)

We have two solutions from \(t(-16t + 90)=0\).

• First solution: \(t = 0\) (corresponds to the time when the ball is kicked).
• Second solution: \(-16t+90 = 0\). Then \(16t=90\), so \(t=\frac{90}{16}=5.625\).

Answer:

\(5.63\)