Question

Unreasonable results A dolphin in an aquatic show jumps straight up out of the water at a velocity of 15.0 m/s. (a) List the knowns in this problem. (b) How high does his body rise above the water? To solve this part, first note that the final velocity is now a known, and identify its value. Then, identify the unknown and discuss how you chose the appropriate equation to solve for it. After choosing the equation, show your steps in solving for the unknown, checking units, and discuss whether the answer is reasonable. (c) How long a time is the dolphin in the air? Neglect any effects resulting from his size or orientation.

a) 11.3 m
b) 17.2 m
c) 22.0 m
d) 27.6 m

Answer 1

The dolphin rises to a height of 11.3 m above the water with an initial velocity of 15.0 m/s. The dolphin is in the air for approximately 1.53 seconds.

Step-by-step explanation:

(a) The known in this problem is the velocity of the dolphin, which is 15.0 m/s.

(b) The unknown is the height the dolphin rises above the water. To solve for this, we can use the equation y = v02 / (2g), where y is the height, v0 is the initial velocity, and g is the acceleration due to gravity. Plugging in the values, we get y = (15.0 m/s)2 / (2 * 9.8 m/s2) = 11.3 m. The answer is reasonable as dolphins can jump several times their length out of the water.

(c) The time the dolphin is in the air can be found using the equation v = v0 + gt, where v is the final velocity, v0 is the initial velocity, g is the acceleration due to gravity, and t is the time. Plugging in the values, we have 0 m/s = 15.0 m/s + (-9.8 m/s2)t. Solving for t, we get t = 1.53 s. The answer is reasonable as the dolphin is in the air for a short duration.