Problem

A swimmer bounces straight up from a diving board…

04:50

Problem 45 Hard Difficulty

A dolphin in an aquatic show jumps straight up out of the water at a velocity of 13.0 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 is the dolphin in the air? Neglect any effects due to his size or orientation.

Answer

(a) Knowns are initial velocity and acceleration.
(b) $y_{\text { max }}=8.6 \mathrm{m}$
(c) $t_{\text { tot }}=2.7 \mathrm{s}$

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Physics 101 Mechanics

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Chapter 2

Kinematics

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Video Transcript

So this problem seems tohave not a lot of information in it. But if you kind of understand the situation or analyze the situation correctly, it turns out we actually know four different things about this dolphin. Um, my suggestion is, if you have a hard time understanding where these numbers come from, students draw a picture. Pictures are super super helpful in solving Kinnah Matics problems, especially if you label the things that you know like velocities and positions and things like that. So given this problem, we actually know the initial velocity is 13.0 meters per second. That's what we're told. We also know that the final position I'm sorry that the initial position of the dolphin and zero meters we can call the surface of the water zero be unjust measure from there because that's where the part of this problem is beginning. Now we know the acceleration is due to gravity, so it's negative 9.8 meters per second squared. But we also know at the very peak of this dolphins jump at its highest point. It momentarily comes to a stop. That's because objects that are thrown upward or that move upward slow down, stop momentarily, then start to speed up in the negative direction as they come back down. So at the very, very highest point of anything's travel, it's going to have a velocity of zero meters per second. That being said, we could use this information to figure out how high the Dalton jumps. So we use all the same information, and the equation that's used is b squared equals initial velocity squared, plus two a X. We plug in our numbers, so the final velocity is zero that's at its highest point. That's equal to 13.0 squared. And then we add that to two times negative 9.8 times X, and we're looking for X here. And when you do your math out, ah, you may want to do it step by step and be really careful that you follow your positives and negatives because that's gonna change your answer if you don't follow those fruit, so you'll find that when it's all said and done, the dolphin travels a to a height of 8.62 meters. Pretty impressive. Now to figure out how much hang time this dolphin has, how much time it's in the air. We use the same information. We just use a different equation. So the equation chosen was that final velocity equals initial velocity plus acceleration. Times time we plug in our numbers. So final velocity of zero when it's at its highest point initial velocity of 13.0 and then we add the negative 9.8 times t and when we saw 13 we see that the time is 1.33 seconds. But we have to pause and think about what this time is for. This time is on Lee, for when the dolphin leaves the water up to its highest point, we want to know how much time this dolphin spends in the air total. So until it comes back down and hits the water because the acceleration due to gravity is constant, it's going to take the same amount of time for the dolphin to go up as it does for it to come back down. So, in order to find the total amount of time we take the time that we solve for 1.33 seconds and we have to multiply by two, we find that it takes the dolphin 2.65 seconds to jump out of the water. Go up too tight point and come back down into the water.

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