Final answer:
To solve the projectile motion problem of the package dropped from the airplane, you calculate the fall time using the free-fall formula, find the final vertical velocity using the acceleration due to gravity and the fall time, and determine the horizontal displacement using the constant horizontal velocity and fall time.
Step-by-step explanation:
Calculating Projectile Motion of a Dropped Package
When an airplane flying with a horizontal initial velocity of 80 m/s drops a package to the ground from an initial height of 490 meters, several steps must be taken to determine the package's fall time, final vertical velocity, and horizontal displacement. First, we calculate the time it takes for the package to hit the ground using the formula for objects in free fall:
time = sqrt((2 * height) / g), where g is the acceleration due to gravity (9.81 m/s2).
Next, we find the final vertical velocity just before the package hits the ground using the equation:
v = g * time
Last, to find the horizontal displacement, we utilize the constant horizontal velocity and the time calculated in the first step:
displacement = horizontal velocity * time.
By following these steps, we can solve all parts of the projectile motion problem related to the package dropped from the airplane.