Final answer:
To calculate the time Carol has to react before the volleyball hits the ground, we use kinematic equations. Using these kinematic equations results in a quadratic formula that provides the time it takes for the volleyball to hit the ground after being served with an initial velocity of 22 ft/s from a height of 3.5 feet.
Step-by-step explanation:
Laura serves a volleyball with an upward velocity of 22 ft/s and the ball is initially 3.5 feet above the ground. We can solve this problem by using the kinematic equations for projectile motion. The formula to find the time it takes for the volleyball to reach the ground is derived from the equation:
s = ut + ½at²
Where:
- s is the displacement (in this case, -3.5 feet since it will be falling below its starting point)
- u is the initial velocity (22 ft/s upward)
- a is the acceleration (due to gravity, which is approximately -32 ft/s² downward)
- t is the time in seconds
Rearranging the equation and solving for t, we can use the quadratic formula. Plugging in the values we get:
–(±)√(22² - 4 × ½ × -32 × -3.5)
From the two possible t values, we discard the negative value since time cannot be negative. Rounding to two decimal places, we find the time Carol has to react before the volleyball hits the ground.