Problem

$\bullet$ $\bullet$ A 2.50 -kg mass is pushed aga…

05:10

Problem 32 Medium Difficulty

$\bullet$ A 72.0 -kg swimmer jumps into the old swimming hole from
a diving board 3.25 m above the water. Use energy conserva-
tion to find his speed just he hits the water (a) if he just holds
his nose and drops in, (b) if he bravely jumps straight up (but
just beyond the board!) at $2.50 \mathrm{m} / \mathrm{s},$ and $(\mathrm{c})$ if he manages to
jump downward at 2.50 $\mathrm{m} / \mathrm{s}$ .

Answer

a) 7.98 $\mathrm{m} / \mathrm{s}$
b) 8.36 $\mathrm{m} / \mathrm{s}$
c) 8.36 $\mathrm{m} / \mathrm{s}$

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Physics 101 Mechanics

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Video Transcript

Okay, Uh, look at this diagram. We see that. Consider that the that's the water on DH. That's the board from where the sermon starts jumping. So for part A, it's given that the swimmer just jumps straight down and there's no initial velocity for it. So let's call this point 0.1, and let's call me. Use a different color point two and ah, let's consider the upward motion as the positive. Why direction is this is 0.1. Then we can say that this is in the kitchen. The feller. This's why one this one is Why, too. Thanks. Then the difference between the board and the water will be why one minus y too. So the height will be why one minus y, too. We consider that a positive direction is upwards and this is the water level. And if we consider that a zero, so why to becomes zero in our case now for part A. So before solving the problem that see what equation will be using. Now we see that if the summaries around here, then he will have some potential energy stored in himself because because of the height when we're considering this as the sea level or level zero. Then there's no potential energy over here when he he jumps in the water. But there will be some velocity because all the potential energy will be converted to kind of big energy. So we can write potential energy around this region and all the potential energy is converted to kind of energy when the summer is around here. Now, if we look at the question 7.11 we see the relation between potential and candidate energy. So from the conservation of potential and Kennedy energy, we see that everything e one squared plus and G why one is equal to half off m v two squared plus mg. Why don't where again as we mentioned that, why two is the total amount of energy at 0.2 and why one is the total amount of energy in 10.1? We mentioned that there is no for party, there's no initial velocity, so the one is zero in our case. Why two is at sea level, So there's no potential energy there, so why do it? Zero. Considering these two facts this term on this time become zero. Now we have m g Y one, which is equal to half off him. The two squared where Vito is the velocity. At this point, we need to solve that and free right Vito in terms ofthe the other terms. Now we can see that we can get it off this M terms from what st. So we'll have square root off two times g times. Why want right using the values? Let me write down the equation one more time, So V two is two times g times y one our given values for why one mg is for G. It's 9.8 meters per second squared for why one? It's 3.25 meter. While we do the calculation, we see that V two is 7.98 You never second for Barbie. The swimmer jump straight up with some initial velocity, so we'll have some initial velocity at this time. So let me lie down that equation one more time so that it's easier to understand we have happened. Be one squared plus M g Y. One is equal to half off and the two squared plus mg. Why, too, as we mentioned that white, who is always zero. So we don't have to worry about this term. This is always zero. Now, this time is not zero because his jumping straight up, sir. And ah, the one is 2.5 meters per second. Why one is given with his 3.25 meters using those values. Now, if we saw for Vito, we see that Vito will be square root off. Let's get rid off this m terms from here. So Vito will be square root off the one squared plus Georgie. Why one? Using the given values, we see that the one is two point 5,000,000 per second. Then whoever square plus two times 9.8 meters per second squared times 3.25 meter for the height. So Vito becomes 8.36 Me never second for part. See, we again have you on as 2.5. I need every second and we see that the other terms won't change that much because we even if we change the direction of the velocity. So for this case, if we invent, if we consider the velocity is positive, we'll have a squared times. So it's quite time over here. So no matter if we take positive and negative, this whole time becomes positive anyway. So for see if we as we mentioned that the upward direction as positive white and since the memory jumping downwards, we can put a negative sign in front of it. But that won't change the result much from B because we have the one squared over here, which is positive terms. That means we can safely say that our results will be same as result in peace. So we too will be in point 36 me over a second. So one thing that we noted here is kind of dignity depends on the speed, not in the direction of the velocity. So kinetic energy is not dependent. Fondi, um direction off the velocity I

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