Final answer:
To find the time it takes for the ball to reach the ground, we can use the position function for free-falling objects. The velocity of the ball when it arrives at the ground can be determined by differentiating the position function with respect to time.
Step-by-step explanation:
To determine the time it takes for the ball to reach the ground, we can use the position function for free-falling objects: s(t) = -16t² + v₀t + s₀. In this case, the ball is thrown straight down from the top of a building, so the initial velocity, v₀, is -30 feet per second and the initial position, s₀, is 435 feet. Plugging in these values into the position function, we get: s(t) = -16t² - 30t + 435.
Now, we can set the position function equal to zero to find the time it takes for the ball to reach the ground: 0 = -16t² - 30t + 435. This is a quadratic equation, so we can solve it by factoring or by using the quadratic formula. Once we find the positive root, we can use it to determine the time it takes for the ball to reach the ground.
To find the velocity of the ball when it arrives at the ground, we can differentiate the position function with respect to time to obtain the velocity function: v(t) = -32t - 30. We can then plug in the time it takes for the ball to reach the ground to find its velocity.