Final answer:
The water balloon thrown downward at an initial speed of 3.5 m/s from an 8.0-meter-high building will hit the sidewalk with a final velocity of approximately 13.0 m/s. The correct answer is not listed in the provided options.
Step-by-step explanation:
If you throw a water balloon downward from the roof of a building at a speed of 3.5 m/s, we must calculate how fast the balloon will be moving when it hits the sidewalk 8.0 m below. To solve this, we use the kinematic equation for objects in free fall under the influence of gravity:
v^2 = u^2 + 2gh
Where v is the final velocity, u is the initial velocity, g is the acceleration due to gravity (9.8 m/s^2 on Earth), and h is the height. Plugging in the values, we get:
v^2 = (3.5 m/s)^2 + 2(9.8 m/s^2)(8.0 m)
v^2 = 12.25 m^2/s^2 + 156.8 m^2/s^2
v^2 = 169.05 m^2/s^2
v = sqrt(169.05 m^2/s^2)
v ≈ 13.0 m/s
The final velocity when the balloon hits the sidewalk would be approximately 13.0 m/s. The correct answer to the multiple-choice question is not provided in the options listed. The closest value is option D) 10.5 m/s, but it is not accurate.