Question

1. pedro kicks a soccer ball from the top of a hill 48 ft. above the ground. the function ( h(t) = -16t^2 + 32t + 48 ) gives the height of the ball ( t ) seconds after it is thrown. how long will it take the ball to reach the ground?

Explanation:

Step1: Set height to 0 (ground level)

$0 = -16t^2 + 32t + 48$

Step2: Simplify the equation

Divide all terms by $-16$:
$t^2 - 2t - 3 = 0$

Step3: Factor the quadratic

$(t - 3)(t + 1) = 0$

Step4: Solve for t

Set each factor to 0:
$t - 3 = 0 \implies t=3$; $t + 1 = 0 \implies t=-1$
Discard negative time.

Answer:

3 seconds