Final answer:
The time it takes for the package to hit the ground is 12.5 seconds. The distance the package traveled horizontally is 1000 meters. The final velocity of the package is -122.5 meters per second.
Step-by-step explanation:
To find the time it takes for the package to hit the ground, we can use the equation:
time = distance / velocity
Since the package is dropped from a height of 1000 m, the distance is 1000 m. The velocity of the plane is 80 m/s. So, the time it takes for the package to hit the ground is:
time = 1000 m / 80 m/s = 12.5 s
To find the distance the package traveled horizontally, we can use the equation:
distance = velocity * time
The velocity of the plane is 80 m/s and the time is 12.5 s. So, the distance the package traveled horizontally is:
distance = 80 m/s * 12.5 s = 1000 m
Finally, to find the final velocity of the package, we can use the equation:
final velocity = initial velocity + (acceleration * time)
Since the package is dropped, its initial velocity is 0 m/s and the acceleration is -9.8 m/s^2 (assuming downward direction is positive). The time is 12.5 s. So, the final velocity of the package is:
final velocity = 0 m/s + (-9.8 m/s^2 * 12.5 s) = -122.5 m/s