The height; in meters, above sea level of a NASA launched rocket is given by h(t) 4.9t2 + 40t + 276 where t represents the number of seconds since the rocket was la...

A rocket is launched in the air. Its height, in meters above sea level, as a function of time, in seconds, is given by $h(t)=-4.9 t^{2}+229 t+234$. a. From what height was the rocket launched? b. How high above sea level does the rocket reach its peak? c. Assuming the rocket will splash down in the ocean, at what time does splashdown occur?

We need to find the maximum high of the rocket using the given quadratic equation. So we need to find the maximum time first using our axis of symmetry. So T. Is equal to negative B over two A. This is A. This is B. And this is C. So we get negative 229 divided by two times negative 4.9. We type that in and that becomes 11 1045 divided by 49. That's our maximum time. So now we're going to evaluate the function H at 1100 45 divided by 49. We get negative 4.9 times 1145 divided by 49 square plus 229 times 1149 divided by 49 plus 234. We get negative 4.9 times 100 and 45 divided by nine square 49. And then plus 229 times 101,000, 145 divided by 49 plus 234 gives us approximately 2000, 909 0.56 and our units are in meters.

This problem goes to say rocket problem. So we have the height function in time. So we have the height of the rocket at any given moment is negative 4.9 t square us to 29 t plus 2 34 And the problem just wants to know what is the maximum height that their object obtained. So leading coefficients negative. We're gonna have a problem pointed down. So it's really just asking us what is the y cordoned off that vortex. So the X coordinate is just gonna be minus B over to a So it's just figure that out so quick it's it's going negative to 29 over negative 9.8. Okay. And that's gonna give us, uh, kind of long decimal just 23 seconds. So I'm gonna store that my calculator, but it's 23 points and more eso, but that's just our time. So we need to plug that back into the equation. So if I play that back and I have this age of this is the variable saved on my calculator, So this is gonna be negative. 4.9 times that number squared plus 2 29 times that number plus 2 34 Okay, let's punch that in. That number comes out to be 29. 09 25 6 And then that's gonna be in meters. So it goes to more decimal places, but here we go. So after playing in our value of tea, which is around 23 seconds, Um, and I just saved that in my calculator stuff. Wouldn't, like round off the decibels. Uh, our final answer here is just gonna be 29 2909 meters. Thank you.

So we want to find the solution of F. T equals zero. We can use Newton's method. First we find the derivative of F. T. And then we can use Newton's method. We use this data radio formula here for this fracturing and numerous story is just F excess and the denominator is F. Prime Erickson First he said the initial value to zero. And we substitute Accent with zero. We get X one, substitute Excellent with X. one x 2. And we can repeat this process refunds. That the value is negative .0021. And it does not change. And so we should change the initial value since we know T. Must be greater than or equal to zero. And if it sells the unusual battle to 50 and we repeat this iterative process. And after six Iterations The video does not change anymore. Energy is 60 points 9385.

According to the question, the height off launch object is given as a quadratic with respect could empty. So let's assume the quadratic is 80 square plus B d plus c. Okay, so if we'll get a B and C, then we know everything about this quantity. Prove it. So again, what is given in the question is a dynasty dance. When the object is launched, the height of the object from sea level is 64 and time could t second. The height is again 64 because off the treaties again, the launching high and the last information is at times stance five. The objectives diving into the sea so the Hyde will be zero. So let's use this information to get a B and C So I'm using first in for a reason. Head off zero Could do a times zero square. Bless many times, dear. A policy could you see that is given 64 in the question. Okay. Then used the second front. Listen at up to use 64 a into three squared plus me into three. Plessy could do 90 less creamy. Plus C C is 64 from the previous information, so we can put a girl do 64 so long we can relight it as three A plus me could do. Zero. This is a very Christian American. Okay, They looked hard and fluorescent is at off five to zero tons. Eight times five square plus me times five plus c 25 plus. Find me plus 64. It was. The new C 64 is equal to zero. This is our secondly kissing. So do get a b and C we have to eliminate be from because Enomoto severe calculating cinema to minus five times kissing a Marilyn. Okay, so the result will be 25 e plus five b less 64 minus 15 a minus five B called a zero. Still from here. Danny plus 64 will be zero, so we can say equal to minus 6.4. Okay, good. It's off. Will put Hey him Chris in number one, you get, We could do minus three. There. Dis minus three times minus explained for So we'll get. Be called 19.2. Okay, so now we have a me and see so we can write our quite like a ticking for missing again. that is edge off the equal. Do minus 6.4. Be square plus 19 point duty plus 64. So from here, it off d being maximum at. He could do minus B a bone. Do it that this minus 19 point do a bowling. Two times minus 6.4. Okay, so the answer will be when burned. Five seconds, so you can see it at the time. Instance off. 1.5. Security. The launch objective be actor highest point.