Respuesta :
Answer:
The taken by Rhonda to react before volleyball hits ground is 2.39 seconds
Step-by-step explanation:
Given as :
The upward velocity of the volleyball = 14.5 ft/s
The height of the ball above ground = 4 feet
Consider value of acceleration due to gravity = 9.8 m/s
Let the time for Rhonda to react before ball hits ground = t sec
Now,
S = u t + [tex]\frac{1}{2}[/tex] a t²
where s = height
u = initial velocity , a = acceleration due to gravity , t = time in sec
So, 4 = 14.5× t + [tex]\frac{1}{2}[/tex] × 9.8 × t²
or, 4 = 14.5 t + 4.9 t²
or, 4.9 t² + 14 .5 t - 4 = 0
Now, solve for t
t = [tex]\frac{-b\pm \sqrt{b^{2}-4\times a\times c}}{2\times a}[/tex]
or, t = [tex]\frac{-14.5\pm \sqrt{14.5^{2}-4\times 4.9\times (4)}}{2\times 4.9}[/tex]
Or, t = [tex]\frac{-14.5\pm \sqrt{80.5025}}{9.8}[/tex]
Or, t = - 2.39 , - 2.76
Hence The taken by Rhonda to react before volleyball hits ground is 2.39 seconds . Answer
