Marsha serves the volleyball to Sharon with an upward velocity of 21ft/s
. The ball is 3.5 feet above the ground when she strikes it. How long does Sharon have to react, before the volleyball hits the ground? Round your answer to two decimal places.
The time it takes for the volleyball to hit the ground is equal to the time it takes for the ball to reach its maximum height.
Using the equation for the vertical motion of a projectile, we can calculate the time it takes for the ball to reach its maximum height.
t = (2*v)/g
where t is the time, v is the initial velocity, and g is the acceleration due to gravity (32 ft/s^2).
t = (2*21)/32
t = 1.3125 seconds
Therefore, Sharon has 1.31 seconds to react before the volleyball hits the ground.
answered is assuming she hit it at ground level
AAAaannndd the bot gets it wrong yet again!
h = 3.5 + 21t - 16t^2
h=0 when t=1.46
To find the time Sharon has to react before the volleyball hits the ground, we can use the fact that the time it takes for an object to fall to the ground can be determined using the formula:
t = sqrt((2h)/g)
where:
t = time (in seconds)
h = height (in feet)
g = acceleration due to gravity (32.2 ft/s^2)
In this case, the height from which the ball is struck (h) is given as 3.5 feet.
Putting the values into the formula, we have:
t = sqrt((2 * 3.5) / 32.2)
Evaluating the expression, we get:
t = sqrt(7 / 32.2)
t ≈ 0.424 seconds
Therefore, Sharon has approximately 0.42 seconds to react before the volleyball hits the ground.