Final answer:
The soccer ball takes 3 seconds to return to the ground.
Step-by-step explanation:
The quadratic function y=-16t^2+48t represents the height (y) of the soccer ball at time (t) seconds. To find the time it takes for the soccer ball to return to the ground, we need to find the value of t when y = 0.
Plug in y = 0 into the equation: -16t^2 + 48t = 0.
Factor out a common factor of 16t: 16t(-t + 3) = 0.
Set each factor equal to zero and solve for t: 16t = 0 or -t + 3 = 0.
The first equation gives us t = 0, which represents the time when the soccer ball is initially kicked. The second equation gives us -t + 3 = 0, which gives us t = 3.
Therefore, it takes 3 seconds for the soccer bal to return to the ground.