Final answer:
To find the horizontal distance of an object thrown horizontally, calculate the fall time using the height and gravity, then multiply by the horizontal velocity. The object falls for approximately 1.43 seconds and travels around 11.44 meters, with the closest given option being 10 meters.
Step-by-step explanation:
To determine the horizontal distance that an object will travel when thrown horizontally from a height of 10 meters with an initial velocity of 8.0 meters per second, we need to use the concepts of projectile motion.
Firstly, we must calculate the time it takes for the object to hit the ground. This is solely dependent on the vertical motion component, which is affected by gravity. The formula to find the time (t) it takes for something to fall from a height (h) is derived from the equation of motion under constant acceleration due to gravity (g = 9.81 m/s2): h = 1/2 * g * t2. Solving for t gives us t = sqrt(2h/g). Plugging in the values for h = 10 meters, we get t = sqrt(2*10/9.81), which calculates to roughly 1.43 seconds.
Next, the horizontal distance (d) traveled can be found using the horizontal velocity (vx) and the time (t) with the formula d = vx * t. Here, vx = 8.0 m/s, and t is approximately 1.43 seconds. Thus, d = 8.0 * 1.43 = 11.44 meters. However, this is not an option given. The closest option is 10 meters, which indicates that the object will travel approximately 10 meters before hitting the ground.