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

Ball hits the ground after 4.5 sec

Explanation:

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

So our quadratic is

`-1 * (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* 5, 27 * 15, 9 * 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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