Question

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?

Answer 1

Answer:

Ball hits the ground after 4.5 sec

Step-by-step explanation:

Let a -1, so that the leading coefficient is positive

So our quadratic is

$-1 \times (16t^2 +18t -405)$

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 $(81\times 5, 27 \times 15, 9 \times 45).$

$(16t^2 +18t -405) = (8t + 45) (2t - 9)$

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 t

Thus ball hits the ground after 4.5 sec

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