SOLUTION: A falling object travels a distance given by the formula d = 5t + 16t2 , where d is measured in feet and t is measured in seconds. How many seconds will it take for the object to t

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Question 1038483: A falling object travels a distance given by the formula d = 5t + 16t2 , where d is measured in feet and t is measured in seconds. How many seconds will it take for the object to traveled 94 ft?
Answer by Othel(27) About Me  (Show Source):
You can put this solution on YOUR website!
We have been given the distance in this equation, which means that the only variable left is t. So we will plug in the distance and get...
94=5%2At%2B16%2At%5E2
I am hoping that you have already studied quadratic equations, as the easiest method of calculating the answer lies in the derivation of the quadratic formula...
%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a
We can subtract 94 from each side of our equation, and rearrange a little according to the commutative property of addition, and we have...
16t%5E2%2B5t-94=0
And then simply plug the numbers into the quadratic formula...
%28-5%29%2B-sqrt%285%5E2-4%2A16%2A%28-94%29%29%2F%282%2A16%29
From this we get...
%28-5%2B-sqrt%286041%29%29%2F32
using a calculator, we find that...
t is approximately 2.27, rounded to the hundredth.
and,
t is approximately -2.59, rounded to the nearest hundredth.
Since we know that time must be a positive number, then we can say that the falling object travels 94 feet in approximately 2.27 seconds.
Check your answer! Plug the value for t into the original equation...
I hope this helps. Learn on