A helicopter is ascending (moving upwards) at a constant velocity of 8 m/s. At a height of 90m, a passenger opens a window and drops a package to the ground below. How long does it take the package to hit the ground and how fast is it moving just before impact?

To solve this problem, we can use the equations of motion. Here are the steps to find the time it takes for the package to hit the ground and its final velocity:

Step 1: Find the time it takes for the package to reach the ground.

We know that the helicopter is ascending at a constant velocity of 8 m/s, which means the package will also have this velocity initially. The height from which the package is dropped is 90 meters. We can use the equation of motion for vertical motion:

h = ut + (1/2)gt^2

where:
h = height
u = initial velocity
g = acceleration due to gravity (approximated as 9.8 m/s^2)
t = time

Plugging in the values, the equation becomes:

90 = 8t + (1/2)(9.8)t^2

Simplifying the equation, we get:

4.9t^2 + 8t - 90 = 0

We can solve this quadratic equation to find the time t. The solutions will be the time it takes for the package to reach the ground.