Question

a volleyball player has spiked the ball. At the instant the ball leaves her hand, it is 2.6 m above the ground and has an initial vertical velocity of -20 m/s. How long will it take the ball to strike the ground if the opposing team doesn't block it?

Answer 1

Answer: 29.48 s

Explanation:

Given

The initial height of the ball is $h=2.6\ m$

The ball leaves with an initial velocity of $u=-20\ m/s$

Using the equation of motion

$h=ut+\dfrac{1}{2}at^2\\\text{Insert the values}\\\\2.6=20\cdot t+\dfrac{1}{2}\times 9.8\times t^2\\\\\Rightarrow 9.8t^2+20t-5.2\\\\\Rightarrow t=\dfrac{-20\pm \sqrt{20^2-4\times 9.8\times (-5.2)}}{2\times 9.8}\\\\\Rightarrow t=\dfrac{-20\pm 603.84}{19.8}\\\\\Rightarrow t=29.48\ s\quad [\text{Neglecting negative t}]$

Therefore, it take 29.48 s for ball to reach the ground.