So I have this question that I have no idea how to approach, it was one of my math problems that belong in the category of factoring general quadratics, but I didn't know how to factor it: The equation \(y=-4.9t^2+42t+18.9\) describes the height (in meters) of a ball tossed up in the air at 42 meters per second from a height of 18.9 meters from the ground, as a function of time in seconds. In how many seconds will the ball hit the ground?
+26367 So I have this question that I have no idea how to approach,
it was one of my math problems that belong in the category of factoring general quadratics,
but I didn't know how to factor it:
The equation
\(\large{y=-4.9t^2+42t+18.9 }\)
describes the height (in meters) of a ball tossed up in the air at 42 meters per second from a height of 18.9 meters from the ground,
as a function of time in seconds.
In how many seconds will the ball hit the ground?
\(\text{Hit the ground means $y=0\ !$}\)
\(\begin{array}{|rcll|} \hline -4.9t^2+42t+18.9 &=& 0 \quad | \quad \cdot(-1) \\ 4.9t^2-42t-18.9 &=& 0 \\\\ t &=& \dfrac{42\pm \sqrt{42^2-4\cdot 4.9 \cdot (-18.9) } } {2\cdot 4.9} \\ t &=& \dfrac{42\pm \sqrt{42^2+370.44 } } {9.8} \\ t &=& \dfrac{42\pm \sqrt{1764+370.44 } } {9.8} \\ t &=& \dfrac{42\pm \sqrt{2134.44 } } {9.8} \\ t &=& \dfrac{42\pm 46.2 } {9.8} \quad | \quad t>0\ !\\ t &=& \dfrac{42{\color{red}+} 46.2 } {9.8} \\\\ t &=& \dfrac{88.2 } {9.8} \\ \mathbf{ t } & \mathbf{=} & \mathbf{9\ \text{seconds} } \\ \hline \end{array}\)
In 9 seconds the ball will hit the ground.
