Final answer:
To find the launching velocity of the balloon with a hang time of 14 s, we apply the kinematic equation with half of the hang time, which gives us a calculated velocity much greater than the available options, suggesting a possible typo in the provided choices.
Step-by-step explanation:
The question is asking about the initial launching velocity of a balloon that has a hang time of 14 s before it comes to rest and starts falling back down. We can use the kinematic equation for uniformly accelerated motion without initial velocity, which is v = at, where v is the final velocity, a is the acceleration due to gravity (9.8 m/s2), and t is the time taken to reach the highest point. Since the total hang time is given for the entire trip (up and down), we would divide it by 2 to get the time to the highest point. Calculating this gives us a launching velocity v = 9.8 m/s2 x (14 s / 2) = 68.6 m/s, which means the closest option listed which can be considered a typo is (b) 19.6 m/s if we assume an error in the provided options.