SOLUTION: I am completely lost! Please Help? If a stone is tossed from the top of a 350 meter building, the height of the stone as a function of time is given by h(t) = -9.8t2 – 10t + 350

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I am completely lost! Please Help? If a stone is tossed from the top of a 350 meter building, the height of the stone as a function of time is given by h(t) = -9.8t2 – 10t + 350      Log On


   

Question 387764: I am completely lost! Please Help?
If a stone is tossed from the top of a 350 meter building, the height of the stone as a function of time is given by h(t) = -9.8t2 – 10t + 350, where t is in seconds, and height is in meters. After how many seconds will the stone hit the ground? Round to the nearest hundredth’s place; include units in your answer
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
h%28t%29+=+-9.8t%5E2+-+10t+%2B+350
Height is measured from the ground up. So when the stone hits the ground, its height will be zero. So the equation to solve is:
0+=+-9.8t%5E2+-+10t+%2B+350
This is a quadratic equation. We already have a zero on one side so we proceed to the next step: Factor or use the Quadratic Formula. The expression on the right side will not factor so we must use the Quadratic Formula:
t+=+%28-%28-10%29+%2B-+sqrt%28%28-10%29%5E2+-+4%28-9.8%29%28350%29%29%29%2F2%28-9.8%29
which simplifies as follows:
t+=+%28-%28-10%29+%2B-+sqrt%28100+-+4%28-9.8%29%28350%29%29%29%2F2%28-9.8%29
t+=+%28-%28-10%29+%2B-+sqrt%28100+%2B+13720%29%29%2F2%28-9.8%29
t+=+%28-%28-10%29+%2B-+sqrt%2813820%29%29%2F2%28-9.8%29
t+=+%2810+%2B-+sqrt%2813820%29%29%2F%28-19.6%29
t+=+%2810+%2B-+sqrt%284%2A3455%29%29%2F%28-19.6%29
t+=+%2810+%2B-+sqrt%284%29%2Asqrt%283455%29%29%2F%28-19.6%29
t+=+%2810+%2B-+2%2Asqrt%283455%29%29%2F%28-19.6%29
t+=+%28100+%2B-+20%2Asqrt%283455%29%29%2F%28-196%29
t+=+%284%2825+%2B-+5%2Asqrt%283455%29%29%29%2F%284%2A%28-49%29%29
t+=+%28cross%284%29%2825+%2B-+5%2Asqrt%283455%29%29%29%2F%28cross%284%29%2A%28-49%29%29
t+=+%2825+%2B-+5%2Asqrt%283455%29%29%2F%28-49%29
In long form this is:
t+=+%2825+%2B+5%2Asqrt%283455%29%29%2F%28-49%29 or t+=+%2825+-+5%2Asqrt%283455%29%29%2F%28-49%29
The first equation gives us a negative value for t (because the numerator will be positive and the denominator is negative). Since time cannot be negative, we will reject the solution from that equation. So the only meaningful solution is:
t+=+%2825+-+5%2Asqrt%283455%29%29%2F%28-49%29
This is an exact expression for the solution. If you want a decimal approximation then get out your calculator, find the square root and simplify the expression.