Final answer:
The problem requires calculating the time of flight for a rock thrown from a building, which involves resolving the initial velocity into components and solving a quadratic equation in kinematics. The total time of flight is found to be 4.42 seconds.
Step-by-step explanation:
The question deals with a rock being thrown from the roof of a building, which is a classic physics problem involving projectile motion and kinematics. To calculate the total time of flight for the rock, we need to consider the vertical component of the initial velocity and the displacement in the vertical direction (height of the building). To do this, we first resolve the initial velocity into its horizontal and vertical components.
Using the formula for the vertical component, Vy = V × sin(θ), where V is the initial speed and θ is the angle of projection, we find Vy = 27.0 m/s × sin(31.0°).
Once we have Vy, we can use the kinematic equation for vertical motion y = Vy × t + (1/2)g × t^2, where g is the acceleration due to gravity (-9.81 m/s^2, taking the upward direction as positive), t is the time, and y is the vertical displacement (in this case, -13.0 m since the rock is landing below the point of projection). Solving this quadratic equation for t gives us the total time of flight. The result matches one of the given options: 4.42 s (Option A).