The height h in feet of an object after t seconds is given by the function
h = –16 t^2 + 60t + 9
How long will it take the object to hit the ground? Round your answer to the nearest thousandth.
2007-04-14 17:00:27 · 11 answers · asked by Mr.Archie G 2 in Science & Mathematics ➔ Mathematics
Set h=zero and solve the quadratic or use a quadratic solver.
I get x1=-0.144, x2=3.894
It must be x2 because time must be positive.
2007-04-14 17:04:10 · answer #1 · answered by T & A 1 · 1⤊ 0⤋
You are looking for when h = 0 because that's ground level.
0 = -16t^2 + 60t + 9
I like to get rid of the negative in front.
0 = 16t^2 - 60t - 9
t = -b ± √(b^2 - 4(a)(c)) / 2a
t = 60 ± √(60^2 - 4(16)(-9)) / 2(16)
t = 60 ± √(3600 + 576) / 32
t = 60 ± √(4176) / 32
t = 60 + √(4176) / 32 =
t = 60 - √(4176) / 32 =
You can plug it into a calculator.
2007-04-14 17:16:00 · answer #2 · answered by its_victoria08 6 · 0⤊ 0⤋
The object is on the ground when its height is 0. So
0 = -16t² + 60t + 9
0 = 16t² - 60t - 9
t = [60 +- sqrt (3600 - 4*16*-9)] / 32
t = [60 +- sqrt 4176]/32
t = 3.894 seconds (the other answer was negative)
2007-04-14 17:12:38 · answer #3 · answered by Kathleen K 7 · 1⤊ 0⤋
Give more details... the value of ur height...
If u want the answer in terms of height, then here's the solution
16t^2 - 60t + (h - 9) = 0
t = 60 +or - sqrt(3600 - 64(h-9))
2007-04-14 17:08:50 · answer #4 · answered by Anonymous · 1⤊ 0⤋
Set h=0 and re-write it as
0=16t²-60t-9
Solve this using the quadratic formula and subrtract the smaller answer from the larger. This will be the total time the object in in the air.
HTH
Doug
2007-04-14 17:09:18 · answer #5 · answered by doug_donaghue 7 · 1⤊ 0⤋
Put h=0 (since it falls to ground)
Solve the quadratic equation -16t^2+60t+9 =0
It will give you the answer.
2007-04-14 17:06:12 · answer #6 · answered by dipakrashmi 4 · 1⤊ 0⤋
Translate what the question is asking you... What is the "height" when the object hits the ground?? (Zero of course). So why not set h = 0 and solve for t?
That means factoring that second order equation into its two roots. Can you factor it into two first order roots (ax + b) and (cx + d)? Or, can you use the Quadratic Formula to get those two roots?
If not, get back to us. IF so, go for it. See what t equals when you set each root equal to zero. Remember that negative t values are insignificant. I suspect you'll get one positive and one negative. THe positive one will be correct.
2007-04-14 17:06:45 · answer #7 · answered by ? 4 · 1⤊ 0⤋
h = -16t^2 + 60t + 9
Set h to zero
-16t^2 + 60t + 9 = 0
This problem is in the form
ax^2 + bx + c = 0
Use the quadratic formula to solve this problem
x = -b + or - sqrt b^2 - 4ac
___________________
2a
In this case,
x = t
a = -16
b = 60
c = 9
Substitute the above values in the formula
t = - 60 + or - sqrt 60^2 - 4 (-16) (9)
________________________
2 (-16)
t = -60 + or - sqrt 3600 + 576
_____________________
-32
t = -60 + or - sqrt 4176
________________
- 32
Please continue, I don't have scientific calculator at hand...
2007-04-14 17:21:05 · answer #8 · answered by detektibgapo 5 · 0⤊ 0⤋
If something is 40% smaller, you in simple terms subtract 40%. So 40% of 40 energy is sixteen: you are trying this by multiplying 40 by 0.4. the respond could be 40 - sixteen = 24 A shorter way could in simple terms be to multiply by 40 by 0.6, by fact it truly is a million-0.4.
2016-12-29 12:12:23 · answer #9 · answered by mahan 3 · 0⤊ 0⤋
If you set h = 0 and work out the quadratic equation, t = 3.894 seconds.
2007-04-14 17:14:46 · answer #10 · answered by teeyore 3 · 1⤊ 0⤋
You need a height from which the object is dropping from in order to answer that question.
2007-04-14 17:03:49 · answer #11 · answered by Joy M 7 · 1⤊ 1⤋