how to get decimal answers

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Joanie10

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I can work the problem right up to the last couple of steps and then I am lost. This is a short reading problem with the formula h= -16t2 +160t +70. A rocket launched from the top of a 40 foot cliff with an initial velocity of 100 ft. per second. The height, h, of the rocket after t seconds is given by the equation: h=-16t2+160t+70. How long after the rocket is launched will it be 40 feet from the ground.
I know the answer to the problem, but do not understand how or where it came from. It was an example to go by. The solutions to the problem is t= -0.4 or t= 10.4 with t= 10.4 as the correct choice. a=-16, b= 160, c= 70.
Using the formula: 40 = -16t2 + 160t +100
0 = -16t2 -160t + 70
t= -160±?(160)2 – 4(-16)(70)/2(-16)
t= -160±?25,600 + 4480/-32
t= -160±?30080/-32
How do you get t= -0.4 or t= 10.4 as answers. I know I can’t use the negative, but how do you get them?
 
Joanie10 said:
I can work the problem right up to the last couple of steps and then I am lost. This is a short reading problem with the formula h= -16t2 +160t +70. A rocket launched from the top of a 40 foot cliff with an initial velocity of 100 ft. per second. The height, h, of the rocket after t seconds is given by the equation: h=-16t2+160t+70. How long after the rocket is launched will it be 40 feet from the ground.
I know the answer to the problem, but do not understand how or where it came from. It was an example to go by. The solutions to the problem is t= -0.4 or t= 10.4 with t= 10.4 as the correct choice. a=-16, b= 160, c= 70.
Using the formula: 40 = -16t2 + 160t +100
0 = -16t2 -160t + 70
t= -160±?(160)2 – 4(-16)(70)/2(-16)
t= -160±?25,600 + 4480/-32
t= -160±?30080/-32
How do you get t= -0.4 or t= 10.4 as answers. I know I can’t use the negative, but how do you get them?
Click to expand...

Your problem statement is not correct.

If the equation given to you is h(t) = -16t[sup:lvib1rpr]2[/sup:lvib1rpr] + 160t + 70

then

initial height CANNOT be = 40 ft

and

initial velocity CANNOT be = 100 ft/sec
 
The problem is verbatim from my math lesson. There are several of these problem all following this example. One of the other problems has a 40 foot cliff, 100 ft. per sec. velosity, and wants to know when the rocket will be 30 feet above the ground. The answer is that it will be there in t = 6.3 seconds. The rocket is falling. That is why the question is so confusing. It does not state that, but it is the only conclusion you can come to. In another part of the lesson this is hinted at, but no where near the problem itself is this stated. Hopes this helps.
 
Okay, mystery solved. In typing the equation after inputting the written problem, I then wrote 100 in the equation formula itself when it should have been 60. I forgot that 40 had to be subtracted from both sides. I was typing one thing while thinking of another. When I took a word-by-word look at the written problem example and its explanation, I saw that I had typed in the wrong number. When I made the correction, the problem is solved to match the the answers I managed to type in correctly. And the decimal answer was no problem. My bad, sorry. Thanks for your time. Maybe my mess-up will remind others to triple check for typos.
 
Joanie, I noticed from you attempt at solving the quadratic that you can go a little SIMPLER.
If equation is -16t^2 + 160t + 70 = 0 :
start by multiplying by -1 to change signs (easier):
16t^2 - 160t - 70 = 0
Divide by 2 (easier to handle):
8t^2 - 80t - 35 = 0
Now use the quadratic.

> Maybe my mess-up will remind others to triple check for typos.
It'll remind ME anyway !
 
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