To find the total time of flight of the ball, we can use the kinematic equation that relates the displacement, initial velocity, time, and acceleration.
In this case, the ball is thrown upward, so the acceleration due to gravity acts in the opposite direction. We can take the acceleration due to gravity as -9.8 m/s².
The initial velocity (u) of the ball is 30 m/s (upward) and the displacement (s) is 40 m (upward).
Using the equation:
s = ut + (1/2)at²
Substituting the known values:
40 = (30)t + (1/2)(-9.8)t²
Simplifying the equation:
40 = 30t - 4.9t²
Rearranging the equation:
4.9t² - 30t + 40 = 0
Now, we can solve this quadratic equation for 't'.
Using the quadratic formula:
t = (-b ± √(b² - 4ac)) / 2a
In this case, a = 4.9, b = -30, and c = 40.
t = (-(-30) ± √((-30)² - 4 * 4.9 * 40)) / (2 * 4.9)
t = (30 ± √(900 - 784)) / 9.8
t = (30 ± √116) / 9.8
Now, calculating the two possible values for 't':
t₁ = (30 + √116) / 9.8 ≈ 4.289 seconds t₂ = (30 - √116) / 9.8 ≈ 0.652 seconds
Since the ball is thrown upward and returns to the initial height, we discard the negative value of time (t₂).
Therefore, the total time of flight of the ball is approximately 4.289 seconds.