a baseball player swings and hits a pop fly straight up in the air to the catcher. the height of the…

a baseball player swings and hits a pop fly straight up in the air to the catcher. the height of the baseball in meters t seconds after it is hit is given by the quadratic function h(t)= - 4.9t² + 14.7t + 1. how long does it take for the baseball to reach its maximum height? what is the maximum height obtained by the baseball? it takes second(s) for the baseball to reach its maximum height. (round to one decimal place as needed.) the maximum height obtained by the baseball is meters. (round to three decimal places as needed.)

a baseball player swings and hits a pop fly straight up in the air to the catcher. the height of the baseball in meters t seconds after it is hit is given by the quadratic function h(t)= - 4.9t² + 14.7t + 1. how long does it take for the baseball to reach its maximum height? what is the maximum height obtained by the baseball? it takes second(s) for the baseball to reach its maximum height. (round to one decimal place as needed.) the maximum height obtained by the baseball is meters. (round to three decimal places as needed.)

Answer

Explanation:

Step1: Identify coefficients

For the quadratic function $h(t)=-4.9t^{2}+14.7t + 1$, $a=-4.9$, $b = 14.7$, $c = 1$.

Step2: Find time to reach maximum height

The time $t$ at which the quadratic - function $y = ax^{2}+bx + c$ reaches its maximum (when $a\lt0$) is given by $t=-\frac{b}{2a}$. Substitute $a=-4.9$ and $b = 14.7$ into the formula: $t=-\frac{14.7}{2\times(-4.9)}=\frac{14.7}{9.8}=1.5$ seconds.

Step3: Find maximum height

Substitute $t = 1.5$ into the function $h(t)=-4.9t^{2}+14.7t + 1$. $h(1.5)=-4.9\times(1.5)^{2}+14.7\times1.5 + 1$. First, calculate $-4.9\times(1.5)^{2}=-4.9\times2.25=-11.025$. Then, calculate $14.7\times1.5 = 22.05$. So, $h(1.5)=-11.025+22.05 + 1=12.025$ meters.

Answer:

It takes 1.5 second(s) for the baseball to reach its maximum height. The maximum height obtained by the baseball is 12.025 meters.