Question

Sharon serves the volleyball to Rhonda with an upward velocity of 18.5ft/s. The ball is 4.5 feet above the ground when she strikes it. How long does Rhonda have to react, before the volleyball hits the ground? Round your answer to two decimal places.

Answer 1

Rhonda has approximately 0.35 seconds to react before the volleyball hits the ground.

Step-by-step explanation:

To calculate the time Rhonda has to react before the volleyball hits the ground, we can use the equation of motion: h = ut + (1/2)gt^2, where h is the initial height, u is the initial velocity, g is the acceleration due to gravity, and t is the time. In this case, the initial height is 4.5 feet, the initial velocity is 18.5 ft/s, and the acceleration due to gravity is 32.2 ft/s^2 (assuming down is positive). Plugging in these values, we can solve for t:

4.5 = 18.5t + (1/2)(32.2)t^2

By rearranging the equation and solving for t, we can find the time it takes for the volleyball to hit the ground.

t^2 + (37/9)t - 6/19 = 0

Using the quadratic formula, we find that t is approximately 0.35 seconds or 0.90 seconds. However, since we are only interested in the time it takes for Rhonda to react, we will consider the positive value of t, which is 0.35 seconds. Therefore, Rhonda has approximately 0.35 seconds to react before the volleyball hits the ground.