a baseball player throws a ball with an initial vertical velocity of 55 feet per second from a height of 6.5…

a baseball player throws a ball with an initial vertical velocity of 55 feet per second from a height of 6.5 feet. use the vertical motion model, (h = - 16t^{2}+vt + s) where (v) is the initial velocity in feet per second and (s) is the height in feet, to calculate how long the ball will be in the air for. round your answer to the nearest tenth. time in the air: ______ seconds enter the answer

a baseball player throws a ball with an initial vertical velocity of 55 feet per second from a height of 6.5 feet. use the vertical motion model, (h = - 16t^{2}+vt + s) where (v) is the initial velocity in feet per second and (s) is the height in feet, to calculate how long the ball will be in the air for. round your answer to the nearest tenth. time in the air: ______ seconds enter the answer

Answer

Explanation:

Step1: Identify values for formula

Given $v = 55$, $s=6.5$, and when the ball hits the ground $h = 0$. So the equation becomes $0=-10t^{2}+55t + 6.5$.

Step2: Use quadratic formula

The quadratic formula for $ax^{2}+bx + c=0$ is $t=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. Here $a=-10$, $b = 55$, $c = 6.5$. First, calculate the discriminant $\Delta=b^{2}-4ac=(55)^{2}-4\times(-10)\times6.5=3025 + 260=3285$.

Step3: Find the values of t

$t=\frac{-55\pm\sqrt{3285}}{-20}$. We have two solutions for $t$: $t_1=\frac{-55+\sqrt{3285}}{-20}$ and $t_2=\frac{-55 - \sqrt{3285}}{-20}$. Since time cannot be negative, we consider the positive - valued solution. $\sqrt{3285}\approx57.31$, so $t=\frac{-55 + 57.31}{-20}$ is incorrect. The correct one is $t=\frac{-55-57.31}{-20}=\frac{-112.31}{-20}=5.6155\approx5.6$.

Answer:

$5.6$