To determine the values of t (time) for which the ball's height is 22 feet, we need to use the equation that describes the height of the ball as a function of time.
The equation for the height of a ball in free fall can be expressed as:
h(t) = -16t^2 + v0t + h0
Where:
h(t) is the height of the ball at time t,
v0 is the initial upward velocity of the ball,
h0 is the initial height of the ball.
Given the values:
v0 = 44 ft/s (initial upward velocity)
h0 = 2 ft (initial height)
We want to find the values of t when h(t) = 22 ft.
Plugging in the values into the equation:
22 = -16t^2 + 44t + 2
Now, let's rearrange the equation to solve for t:
16t^2 - 44t + 20 = 0
To solve this quadratic equation, we can factor it:
4(4t^2 - 11t + 5) = 0
Now, solve the quadratic equation:
4t^2 - 11t + 5 = 0
Factoring further:
(4t - 5)(t - 1) = 0
Setting each factor equal to zero:
4t - 5 = 0 or t - 1 = 0
Solving for t in each case:
4t = 5 or t = 1
Dividing by 4:
t = 5/4
Therefore, the two values of t for which the ball's height is 22 feet are t = 5/4 seconds and t = 1 second.