We need to find those values of t for which h(t) = 97. This means we have to solve 215*t - 16*t^2 = 97. Subtracting 97 from both sides, we get 215*t - 16*t^2 - 97 = 0. Rearranging terms to get the quadratic in standard form, we get -16*t^2 +215*t - 97. I sure don't know the factors off-hand, but I do know how to find them. The quadratic formula. The general form of a quadratic equation is a*x^2 + b*x + c = 0. For our problem, we have

a = -16, b = 215, and c = -97. From quadratic formula, x = [-b +/- sqrt(b^2 - 4*a*c)]/2*a. Plugging in, we get

x = [-215 +/ sqrt((-215)^2 - 4 * (-16) * (-97))]/(2 * (-16) = [-215 +/ sqrt(46225 - 6208)]/(-32), so

x = [-215 +/ sqrt(40017)]/(-32)

x ~ [-215 +/- 200.043]/(-32) so x ~ (-215 - 200.043)/(-32) or x ~ (-215 + 200.043)/(-32), so

x ~ -415.043/(-32) or x ~ -15.053/(-32).

You can calculate these two positive roots.

May 19th, 2015

The solution was given in terms of x rather than t, but the value to t would same as the value of x.