Question

-16t^2 + 800t=6200

Answer 1

Let me guess, you want the maximum height and the time it reaches to get there?

The time it takes t=25s,

Your max height is 3800 [m].

Answer 2

yeah...can you show the steps please?

Answer 3

A rocket is hot upward with at 800 ft/sec and the height of the rocket is given by the function H=-16t^2 = 800t.

a. When does the rocket fall back to the ground level?
b. When does the rocket reach a height of 6200 feet?
c. When does the rocket reach a height of 2 miles?
d. What is the highest point that the rocket reaches?

Answer 4

You use the derivative and differentiate your function, y=-16t^2+800t-6200, and you get y'=32t-800; Now you solve for y'=0, and you get t=(800/32)=25;

This will give you the time it takes to the maximum point.

You replace that in the main equation

y(t) = -16t^2 + 800t -6200 and you get
y(25) = 3800

Shane, please help me, where am I wrong?

Answer 5

a) Set H to 0 and solve for t. You will get two answers with one being 0...the other is the time it takes to land.
b) Set H to 6200 and solve for t again...you should get only one positive value.
c) Set H to (2*5280ft) and solve for t as in b above
d) There are two ways to solve that part...want the calculus one or the other?

Answer 6

@gezimbasha: I retract my earlier response...I missed a subtraction of the 6200

Answer 7

okay, thanks! how do I solve b...can you show me the steps? or did gezimbasha did it right?
For d yeah the calculus one ...what else is there?

Answer 8

Let's go back one step just to make sure I have the right initial equation. Is it this?:\[H=-16t^2 + 800t. \]

Answer 9

No @Shane_B it was my mistake. The correct initial equation is H = -16t^2 + 800t. You were correct. @SummerFlies please ignore my answers.

Answer 10

I got confused by the initial post where he included 6200 also...no biggie.

Answer 11

okay! thank you!

Answer 12

Does that mean we're done here? Are you clear as mud on everything?

Answer 13

lol, yeah same mistake here.

Answer 14

actually I want you to show me how to solve this: -16t^2 + 800t=6200

Answer 15

You can either try factoring it or just be lazy like me and use the quadratic formula.

Answer 16

oh haha okay that's what I needed! Thank You so much guys! You've been a real help! :D

Answer 17

Just to clear up any confusion...

Given the initial equation of \[H=-16t^2 + 800t\]
Part a: Basically it hits the ground when H = 0. This will occur at two times...first when it leaves the ground and then when it returns back to it.

Set the equation to 0 and solve for t:\[0=-16t^2 + 800t\]\[t=0s, t=50s\]The time for it to hit the ground will therefore be 50 seconds.


Part b: Just set the height to 6200 and solve the quadratic equation:\[6200=-16t^2 + 800t\]\[t=9.59s,t=40.41s\]Both of those times are accurate...since it passes that point going up and going back down.


Part c: Set the height to 2*5280ft:\[10560=-16t^2 + 800t\]Solving for t gives you an imaginary values...so it will never reach that height.

Part d: The highest point can be calculated in two ways. The simplest in this case is just to take the flight time you found in part a and divide it by 2...so it will be at max height at 25s since it spends just as much time going up as it does going down (think: constant acceleration due to gravity).

The calculus method would be to simply take the derivative of the expression:
\[h=-16t^2 + 800t\]\[h'=-32t+800\]Setting that to 0 (since at max height, the y velocity will be 0), you would also get 25s.

If you want to know the max height that part is easy at this point:\[h=-16(25s)^2+800(25s)=10,000ft\]Notice that 10,000 is just under 2 miles...which verifies your answer in part c.

Answer 18

Wow this is great! Thank You So Much, Shane!

Answer 19

np :)