In this question, we are given the trajectory of the missile. Okay. Starts from a grows up to be, uh, during that process, the it takes eight seconds. And during the process, uh, the acceleration of the rocket increases linearly with time. And then, um, and he goes to eight seconds. Uh, fuel is cut off and then turns 45 degrees to the right, and then it goes in. Project convention goes, uh, from B to D. Okay, so there are four things we need to find, um, treating. You need to find four things you need to find a speed. True. We need to find the height of the missile HB and the speed of the missile at point B. The maximum higher teen and the range are crashes. That d Okay, so for things to find, So to find that speed and high at point B. Okay, so we look at the graph. Um, the linear line is equal to divide protein divide by eight p, which is I t so d V is equal to a d t. And from zero to be the V c go to 02 t hi T d t and we have three equals to 2.5 T square. Okay, Mhm when TV goes through eight seconds, um is equal to B B is 2.5 times eight square. We get 160 m per second. Okay, so there's this VB 80 fi heights B. Yeah, you know that yes. Is equal to Greedy King. Okay, so from zero to ask. Yes. Secret too. Zero to t 2.5 t square beauty. So, uh, as it goes to 2.53 Yeah, he swear. Thank you. Sorry. Mm. When he is equal to eight seconds, as is equal to 2.5 the right tree. Holmes. It's cute. This is 4 to 7. He does. Okay, so this is HB. Uh huh. Next you can find to the projectile motion. Okay, So for the projectile motion, DVB X. Yes. 160 co sign 45 degrees. So this is actually 82 you know, second, yeah, D B B y. Yes. 169. 45 degrees, which is 82 m per second. Okay, using he's off to find Ah, maximum height. 18. Okay, so this is what How we uh, find it. Okay, so you'll be be wide square goes to B B Y square. Last two, they'll come. Why? So, um Then you take upward to be positive. So zero is equal to e. Uh, two square. My name's too hands. 9.81 Time still talk. Why? A daughter y is equal to 82 square. If I buy two times 9.81 calculate this. You get 652 He does. Okay, So H c is he going to H B s? Delta Y. Okay, so for 27 class 652 Um, yeah. If you use exact numbers, then you should be getting, uh, 1079 km. You run to trees? Significant figures. 51 080 m. Okay, which is 1.8 km. Okay, so this is HC. You can use the 1 m or can Okay, he then to find a range are mhm. Mhm. A range R is able to be the x times t. So this tea, uh, he is the time of flight. So that's the thing we need to find us. It was so to find a time of flight be be using. That's why is he going to Ah, we b y p us have a T square. Okay. And by this time, I'm going to take downward to be positive. Yeah, so I have to. The delta y is h b. It's equal to negative. 82 e bus, huh? 9.81 T square. Okay, so, uh, get 4.905 t square minus 82 e. Right now it's 4 to 6.67 because zero so t using the quadratic formula. Uh huh. K 82 square is 12800 That's four times a. It is minus four a. C. But C is negative. So it becomes a plus. He and the anti by buying 9.81 just to eight and calculate your T to be 26.36 seconds or negative. 3.30 seconds. This is not applicable. So range. Because who were the X? M. T? Which is 80 route two times 26.36 when you get 2980 m, which is 2.98 km. Okay, just so this is the range for the missile. And that's all for this question.