Answer:
a) The balloon and the ball will meet after 1.43 s.
b) The ball will reach the balloon at 15.7 m above the ground.
Explanation:
The height of the confetti ball is given by the following equation:
y = y0 + v0 · t + 1/2 · g · t²
Where:
y = height of the ball at time t
y0 = initial height
v0 = initial velocity
g = acceleration due to gravity (-9.8 m/s² considering the upward direction as positive).
The height of the ball is given by this equation:
y = y0 + v · t
Where v is the constant velocity.
When the ball and the ballon meet, both heights are equal. Let´s consider the ground as the origin of the frame of reference so that y0 = 0:
y balloon = y ball
y0 + v · t = y0 + v0 · t + 1/2 · g · t² (y0 = 0)
11 m/s · t = 18 m/s · t -1/2 · 9.8 m/s² · t²
0 = -4.9 m/s² · t² + 18 m/s · t - 11 m/s · t
0 = -4.9 m/s² · t² + 7 m/s · t
0 = t( -4.9 m/s² · t + 7 m/s)
t = 0 and
0 = -4.9 m/s² · t + 7 m/s
-7 m/s / - 4.9 m/s² = t
t = 1.43 s
They will meet after 1.43 s
b) Now let´s calculate the height of the balloon after 1.43 s
y = v · t
y = 11 m/s · 1.43 s = 15.7 m
The ball will reach the balloon at 15.7 m above the ground.
