The equation y 16t 2 18t 405 describes the height in feet of a ball thrown downward at 18 feet per second from a height of 405 feet from the ground as a function of time t in seconds In how many seconds will the ball hit the ground? Express your answer as a decimal rounded to the nearest tenth?

Accepted Solution

Answer:Ball hits the ground after 4.5 secStep-by-step explanation:Let a -1, so that the leading coefficient is positiveSo our quadratic is [tex]-1 \times (16t^2 +18t -405)[/tex]The key coefficients of two binomial variables can be 1 and 16, or 2 and 8, or 4 and 4, for the leading coefficient of 16.Yet they can't actually be 4 and 4 because the linear (x) term coefficient has to be a multiple of 4, which it isn't and leading coefficients 1 and 16 on the binomial factors is not likely. So, 2 and 8 taken as the leading coefficients of  two binomial factors. For constant  405, possible factorizations are [tex](81\times 5, 27 \times 15, 9 \times 45).[/tex][tex] (16t^2 +18t -405) = (8t + 45) (2t - 9)[/tex]Taking first factor, thus we find  negative value for given time t. But  second time equivalent to zero gives the value of 4.5 for tThus ball hits the ground after 4.5 sec.