Final answer:
The problem involves calculating the time it takes for a ball to hit the ground after being thrown upward from a tall building. It requires substituting the given algebraic expressions into kinematic equations for uniformly accelerated motion. The positive root of the quadratic equation resulting from this substitution is the time sought, rounded to three significant figures.
Step-by-step explanation:
Standing on the roof of a building, you throw a ball straight up with an initial speed given by the expression (14.5 + B) m/s, where B equals 5. The building's height is described by the expression (42.0 + A) meters, with A being 14. We need to calculate the time it will take for the ball to land on the ground below after being thrown upwards and then missing the building as it falls down. This is a problem related to the motion under gravity (free fall) and can be solved using the kinematic equations of motion. To find the time it takes for the ball to hit the ground, we first need to substitute the known values into the expressions for initial velocity and building's height: Initial speed = 14.5 + 5 = 19.5 m/s, and building's height = 42.0 + 14 = 56.0 meters. Applying the equations for uniformly accelerated motion, where the acceleration is due to gravity (g = 9.8 m/s2), we solve for the total time of flight. The kinematic equation that is relevant for this case is: s = ut + 0.5gt2 Where s is the total displacement (here, -56.0 meters, assuming upward is positive), u is the initial velocity (19.5 m/s), and g is the acceleration due to gravity (-9.8 m/s2, since it's in the opposite direction of the initial velocity). After applying this equation and finding the roots of the resulting quadratic equation, we will have two times, of which we select the positive one that represents the total flight time till the ball hits the ground. The correct rounding to three significant figures for the time interval will be the final answer.