Answer
t = 17.1 s
Step-by-step explanation
The equation of motion that gives the height of the water balloon at any time is given as
h(t) = ut + ½at²
where
h(t) = Height of the balloon at any time
t = Time
u = Initial velocity of the water balloon = 84 m/s
a = Acceleration due to gravity = -9.8m/s²
We are then told to calculate the time when the balloon hits the ground, that is, when the height is equal to 0.
h(t) = ut + ½at²
0 = 84t + ½(-9.8)(t²)
0 = 84t - 4.9t²
4.9t² - 84t = 0
t (4.9t - 84) = 0
t = 0 OR 4.9t - 84 = 0
4.9t - 84 = 0
4.9t = 84
Divide both sides by 4.9
(4.9t/4.9) = (84/4.9)
t = 17.1 s
The two answers obtained, t = 0 s and t = 17.1 s denote the beginning and end of the water balloon's journey.
Hence, the answer for how long the balloon takes before it hits the ground again is 17.1 s
Hope this Helps!!!