Questioning any two references. Example for 14 page 16 So I encouraged you. Look at that problem first before going to this one just to get an idea of what we're looking for. But the Question 82 states that, as discussed in that previous example on Archerfish by dislodging unspecific insect from its resting place with a stream of water expelled from the fish's mouth. So in my diagram here, my fish Vivian, my origin. Down here, my fish shoots its water up at the insect, which is that black circle. So we supposed the Archerfish sports water with a speed of 2.15 meters per second at the angle of 52 degrees above the horizontal names for beetle on a leaf of a hate. The height was used in the previous example. It's always the same variables. Ah, hate of three centimeters above the water circus. And what horizontal distance from the Beetle should the Archerfish fire if it is to hit the target in the least time? So that's part a big questions will depart at first. Then we'll go to a party. Um, so we know that well, we're doing going how far. Wait, We're horizontal distance. It'll based on what we're given, we can look at the situation and say, Okay, well, that's very easily given by, you know, the English initial velocity of the extraction times time, which would be very easy to do if we knew what the time was. But we don't as of right now, so we need to stall for time, the time it takes for the water to reach that insect. So in most cases, if it doesn't work out for one of the directional equations, look at the other one, and usually that will give you the right answer. So do the same equation, including acceleration. Um, for the white component, we're going for me, the bottom to the top of this nearest upward. So my d white turns positive. My initial velocity is positive as well come shooting upward of the official shooting upward. What makes Hillary should do the gravity, of course, brings it down. Based on our coordinate system was 1/2 g t square. So, looking at this equation, I was gonna rearrange it to see if you have 1/2 g t squared. It's positive minus v not signed. data because the verdict component of our initial velocity is the sine of the angle corresponds to a side angle. Here, this is why minus the not silent e plus the wine which equals zero. Oh, not do I I'm not using the white very well. Sorry. I should've basis with h. Just what we'll do. Just one consistent with my variables here. So the height in which the insect is above the water is age, not d y. So, in the scenario, um, I want to solve her time. I know every other term of this equation, so that's a hint. Every need are quadratic formula. So by doing this, um, you get two solutions, so I use excel to compute this, use whatever format you use. Um, remember, but most cases we get two instances of time here. We have one solution to be 10.3 to 5 seconds, and sometimes we have a negative solution. But here you are a positive one so that both technically are viable the other time being 0.1 eight seconds. So you think about what's happening here. Why we have to. These times it means that at one height the height that we're looking at. Stay here. It occurs at the first time point. It means if it didn't have the insect, it would continue to travel upwards and go, then go back downwards that the other time would be something like this. Here. These are two points in time. Something like this may not be the skill, but that's the idea. Um, the question does say, however, if it doesn't hit the target in the least amount of time. So therefore we must need this time because a shorter So if Well, I guess here my question. I did represent the distance in the extraction simply by D, so I will keep that notation. So this distance is given by the not coast idea my horizontal component of my initial velocity times time which we now found to be this turn here. So sub seeing this value in for time at this point will allow me to calculate the distance that this water sorry that the beetle is in the horizontal component to me. 2.49 centimeters. The three senior figures, of course, 2.49 see him. So the point to 0.0.249 But that's going right back to centimeters, Whichever one you prefer. Both aren't technically correct. And be well, can already don't be at the state's How much time will it be? It'll have to react, but, well, it racks in the time it gets from the fish's mouth to the beetle itself. So that time we found in part a t peaceably 0.1 88 seconds again 236 figures. So a very cooked match time or else that beetle will probably be eaten for lunch.