Question

A plane that is moving 200 m/s drops a package. The package takes 15 seconds to reach the ground.

A) What height was the package dropped from?
B) How far did the plane travel from the time the package was released until the package hit the ground? Is this the same distance the package travels?
C) How fast was the package moving when it hit the ground?

Answer 1

The package was dropped from a height of 1102.5 meters. The distance the plane traveled from the time the package was released until the package hit the ground is 3000 meters. The package was moving at a velocity of 200 m/s when it hit the ground.

Step-by-step explanation:

To determine the height that the package was dropped from, we can use the formula:

height = (1/2) * g * t^2

where g is the acceleration due to gravity (approximated as 9.8 m/s²) and t is the time it takes for the package to reach the ground (15 seconds).

Substituting the values:

height = (1/2) * 9.8 * (15)^2 = 1102.5 meters

The distance the plane traveled from the time the package was released until the package hit the ground is the same as the horizontal distance traveled by the package. This can be calculated using the formula:

distance = velocity * time

Substituting the values:

distance = 200 * 15 = 3000 meters

The package is initially moving horizontally with the same velocity as the plane (200 m/s) and there is no horizontal acceleration. Therefore, its horizontal velocity when it hits the ground remains the same at 200 m/s.