Final answer:
The question requires solving a quadratic equation representing the motion of an object to determine when it hits the ground.
Step-by-step explanation:
The question relates to the physics of motion, specifically to determining when an object hits the ground based on a quadratic equation. The equation given, -16(0.5)²+16(0.5)+96, likely represents the position of the object over time, derived from the kinematic equations for uniformly accelerated motion. To find when the object hits the ground, we would set this equation equal to zero and solve for time, which is the variable implicitly represented here.
In regards to the provided reference information, this seems to address various physics concepts such as Pythagorean theorem to find resultant vectors, initial velocities, distances, collision theory (elastic and inelastic), gravitational work, and kinematic equations.
However, the provided information does not directly align with finding the time at which the object hits the ground from the provided equation. To solve the given equation, we need to apply algebraic methods to solve for the time variable 't' when the height 'h' is equal to zero, indicating that the object has reached the ground.