Final answer:
The balloons are traveling at a speed of 12.05 m/s when they pass Roger's window. The balloons are being released from the fourth floor.
Step-by-step explanation:
To find the speed at which the balloons are traveling when they pass Roger's window, we can first calculate the time it takes for the balloons to fall from the second floor to the sidewalk. We know that the distance from the second floor to the sidewalk is 10 m. Using the equation of motion s = ut + 0.5at^2, where s is the distance, u is the initial velocity, t is the time, and a is the acceleration due to gravity (approximately 9.8 m/s^2), we can solve for t.
10 = 0 + 0.5 * 9.8 * t^2
t = sqrt(10 / 0.5 * 9.8) = 1.42 s
Therefore, it takes 1.42 seconds for the balloons to fall from the second floor to the sidewalk.
Next, we can use the given information that the balloons strike the sidewalk 0.59 s after passing Roger's window. We know the time it takes for the balloons to reach the sidewalk (1.42 s), so we can subtract the time it takes for the balloons to pass the window (0.59 s) to find the time it takes for the balloons to travel the distance between Roger's window and the sidewalk.
Time taken to travel distance = total time - time taken to pass window = 1.42 s - 0.59 s = 0.83 s
Finally, we can find the speed of the balloons by dividing the distance traveled between Roger's window and the sidewalk (10 m) by the time taken to travel that distance (0.83 s).
Speed = distance / time = 10 m / 0.83 s = 12.05 m/s
Therefore, the speed of the balloons when they pass Roger's window is 12.05 m/s.
To determine from which floor the balloons are being released, we can divide the total distance traveled (10 m) by the height of each floor (5.0 m).
Number of floors = total distance / height of each floor = 10 m / 5.0 m = 2 floors
Since Roger's room is on the second floor, we can conclude that the balloons are being released from the fourth floor.