Final answer:
The dolphin needs to achieve a minimum horizontal speed to jump over a bar 4.5 feet away and 5 feet above the water. By distilling information from a related example, the estimated minimum horizontal speed needed is 6 ft/s, which allows the dolphin to cover the horizontal distance in time to clear the bar.
Step-by-step explanation:
The problem at hand involves a dolphin that has to jump over a bar that is 5 feet above the water while starting from a point 4 feet deep. Since the dolphin can jump 14 feet above the water, it has enough vertical ability to clear the height of the bar. As for the horizontal movement, the bar is placed 4.5 feet from the dolphin, and the dolphin can travel a total horizontal distance of 20 feet.
To calculate the minimum horizontal speed required, we need to determine how long it takes the dolphin to reach the height of the bar. The time to reach maximum height would be half of the total airtime since ascent and descent take equal time. Using the provided solution from a similar scenario, where a dolphin jumps out of the water at 13.0 m/s and is in the air for 2.65 seconds, and considering the ratio of distances, we can estimate the time it takes for the dolphin to reach 5 feet. The minimum horizontal speed is then simply the horizontal distance the dolphin must cover (4.5 feet) divided by this time.
Since typical dolphin speeds and jumping abilities are not given in the problem statement, we need to rely on the provided example. We can estimate that, if a dolphin can jump straight up with a speed of 13 m/s and stay in the air for around 2.65 seconds, it could reach a similar horizontal speed