Final answer:
In free-fall motion, an object's position can be described using the position function. To find the time it takes for the object to reach the ground, set the position function to 0 and solve for time. To find the velocity of the object when it arrives at the ground, take the derivative of the position function and evaluate it at the time found in the previous step.
Step-by-step explanation:
In free-fall motion, the position of an object can be described using the position function. This function is given by the equation y(t) = y0 + v0t - 0.5gt2, where y(t) is the position at time t, y0 is the initial position, v0 is the initial velocity, g is the acceleration due to gravity, and t is time.
(a) To find the time it takes for the ball to reach the ground, set the position y(t) to 0 and solve for t. This will give you the time elapsed.
(b) To find the velocity of the ball when it arrives at the ground, take the derivative of the position function with respect to time (dy(t)/dt) and evaluate it at the time found in part (a). This will give you the velocity at that time.