Final answer:
The horizontal distance a package falls before landing can be found by calculating the time taken to fall using the vertical distance and gravity, then multiplying this time by the horizontal velocity of the plane. The velocity of the package just before impact combines the constant horizontal velocity of the plane with the final vertical velocity due to gravity.
Step-by-step explanation:
To determine the horizontal distance the package falls before landing, we need to know how long it takes to hit the ground. Since it's dropped from a height (vertical distance) of 200.0 m and the only vertical motion is because of gravity, we can use the formula for time of free fall: ∙t = √(2 * d / g), where ∙t is the time, d is the vertical distance, and g is the acceleration due to gravity (9.81 m/s²).
The horizontal distance can be found once we know the time it takes to fall: horizontal distance = horizontal speed * time. The plane is moving at 30.0 m/s, so once we find the time, we multiply that by 30.0 m/s to get the horizontal distance.
To calculate the velocity just before impact, we need to combine the horizontal velocity and the final vertical velocity. The final vertical velocity can be found using the equation vf = g * ∙t (where vf is the final vertical velocity).
Both the horizontal velocity (constant at 30.0 m/s since there's no air resistance) and final vertical velocity vector at impact must be combined using the Pythagorean theorem to find the overall velocity of the package just before it hits the ground.