SOLUTION: trying to solve a velocity equation where s=4.9t^2+Vot Velocity = Vo = 20m/s Height = s = 158.4m time = t = which is what we are solving for so...{{{158.4=4.9t^2 + 20t}}}

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: trying to solve a velocity equation where s=4.9t^2+Vot Velocity = Vo = 20m/s Height = s = 158.4m time = t = which is what we are solving for so...{{{158.4=4.9t^2 + 20t}}}       Log On


   

Question 277032: trying to solve a velocity equation where s=4.9t^2+Vot

Velocity = Vo = 20m/s
Height = s = 158.4m
time = t = which is what we are solving for
so...158.4=4.9t%5E2+%2B+20t
I got as far as 4.9t^2 + 20t - 158.4=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
4.9t%5E2+%2B+20t+-+158.4=0 Start with the given equation


49t%5E2+%2B+200t+-+1584=0 Multiply every term by 10 to make every number a whole number (ie move the decimal one spot to the right).


Notice that the quadratic 49t%5E2%2B200t-1584 is in the form of At%5E2%2BBt%2BC where A=49, B=200, and C=-1584


Let's use the quadratic formula to solve for "t":


t+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


t+=+%28-%28200%29+%2B-+sqrt%28+%28200%29%5E2-4%2849%29%28-1584%29+%29%29%2F%282%2849%29%29 Plug in A=49, B=200, and C=-1584


t+=+%28-200+%2B-+sqrt%28+40000-4%2849%29%28-1584%29+%29%29%2F%282%2849%29%29 Square 200 to get 40000.


t+=+%28-200+%2B-+sqrt%28+40000--310464+%29%29%2F%282%2849%29%29 Multiply 4%2849%29%28-1584%29 to get -310464


t+=+%28-200+%2B-+sqrt%28+40000%2B310464+%29%29%2F%282%2849%29%29 Rewrite sqrt%2840000--310464%29 as sqrt%2840000%2B310464%29


t+=+%28-200+%2B-+sqrt%28+350464+%29%29%2F%282%2849%29%29 Add 40000 to 310464 to get 350464


t+=+%28-200+%2B-+sqrt%28+350464+%29%29%2F%2898%29 Multiply 2 and 49 to get 98.


t+=+%28-200+%2B-+592%29%2F%2898%29 Take the square root of 350464 to get 592.


t+=+%28-200+%2B+592%29%2F%2898%29 or t+=+%28-200+-+592%29%2F%2898%29 Break up the expression.


t+=+%28392%29%2F%2898%29 or t+=++%28-792%29%2F%2898%29 Combine like terms.


t+=+4 or t+=+-396%2F49 Simplify.


So the possible solutions are t+=+4 or t+=+-396%2F49


However, since a negative time value doesn't make any sense, we must ignore the value t+=+-396%2F49


So the only solution is t+=+4