Question 812162
This relates to the physics equation, Y=Yo+Vot+.5at^2
This equation is not factorable, so there is no other option to use except through the quadratic formula. (I think the problem may have been typed wrong, so I am making the "a" value -16 instead of 16.)
The equation can be re-written as this:
-16t^2+65t+1=0
a=-16
b=65
c=1
Now, we use the quadratic formula, which is
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
and plug in the respective variables.
{{{t = (-65 +- sqrt( 65^2-4*-16*1))/(2*-16) }}}
This simplifes to {{{ (-65 +- sqrt(4289))/-32 }}}
Nothing can be simplified in the above equation so if you plug in the numbers, your answer should be
t=-0.0153267912541177, 4.07782679125412 because there's always two answers in quadratics.
Time obviously cannot be negative so the answer you are left with is t=4.07782679125412.
Or you can just say t equals about 4 seconds.

Cheers,
-Bryan