Answer:
It takes the package 5.33 s to reach the ground.
Step-by-step explanation:
The equation for the height of the package at a time "t" is as follows:
y = y0 + v0 · t + 1/2 · g · t²
Where:
y = height at time t.
y0 = initial height.
v0 = initial velocity.
t = time.
g = acceleration due to gravity (-9.8 m/s² considering the upward direction as positive).
Initially, the package is moving at 5.13 m/s relative to the ground because it moves with the helicopter. Then, v0 = 5.13 m/s. When the package reaches the ground, its height will be 0 (placing the origin of the frame of reference on the ground). Then, we can calculate the time it takes the package to reach the ground using the equation of height of the package:
y = y0 + v0 · t + 1/2 · g · t²
0 = 112 m + 5.13 m/s · t -1/2 · 9.8 m/s² · t²
0 = -4.9 m/s² · t² + 5.13 m/s · t + 112 m
Solving the quadratic equation:
t = 5.33 s ( the other negative value is discarded because the time can´t be negative).
It takes the package 5.33 s to reach the ground.