A passenger in a helicopter traveling upwards at 20 m/s accidentally drops a package out the window. If it takes 8 seconds to reach the ground, how high to the nearest meter was the helicopter when the package was dropped?

h = Hi + Vi t - 4.9 t^2

0 = Hi + 20 (8) - 4.9(64)

0 = Hi + 160 - 314

Hi = 154 meters

To find the height of the helicopter when the package was dropped, we can use the equation of motion known as the kinematic equation:

h = vi × t + (1/2) × g × t^2

Where:
h is the height of the helicopter when the package was dropped,
vi is the initial upward velocity of the helicopter (20 m/s),
t is the time taken for the package to reach the ground (8 seconds),
g is the acceleration due to gravity (-9.8 m/s^2).

Let's substitute the given values into the equation:

h = (20 m/s) × (8 s) + (1/2) × (-9.8 m/s^2) × (8 s)^2

Now let's solve the equation step by step:

h = 160 m + (1/2) × (-9.8 m/s^2) × 64 s^2
h = 160 m - 313.6 m
h ≈ -153.6 m

The negative sign indicates that the height is below the starting point of the helicopter, which means the package was dropped from a height of approximately 153.6 meters below the helicopter. In other words, the helicopter was 153.6 meters above the ground when the package was dropped.