Position of package when dropped from plane

[katie_alsteen]

Homework Statement

A plane is flying horizontally with speed 148 m/s at a height 4510 m above the ground, when a package is dropped from the plane. The acceleration is 9.8 m/s^2. Neglecting air resistance, when the package hits the ground, the plane will be... ahead, directly above, or behind the package?

Homework Equations

v^2 = vi^2 + .5ax

The Attempt at a Solution

I tried to break it into x and y components, and solve for x in the horizontal direction, but I am really confused. Please help.

 

[rl.bhat]

What is the initial velocity of the package in the y-direction?
How much time the packet takes to reach the ground?

 

[tomcue]

Based on the given information, the package will hit the ground after a certain amount of time, while the plane continues to fly horizontally at a constant speed. Therefore, the plane will be ahead of the package when it hits the ground. This is because the plane has a constant velocity, while the package has an acceleration due to gravity pulling it towards the ground. As the plane continues to fly forward, the package will fall behind due to this acceleration.

To solve for the position of the package when it hits the ground, we can use the equation d = vi*t + 1/2*a*t^2, where d is the distance traveled, vi is the initial velocity, a is the acceleration, and t is the time. In this case, the initial velocity is 148 m/s, the acceleration is 9.8 m/s^2, and the time it takes for the package to hit the ground can be found using the equation d = vi*t + 1/2*a*t^2 = 4510 m. Solving for t, we get a time of approximately 17.9 seconds.

Therefore, after 17.9 seconds, the package will hit the ground and the plane will be 148 m/s * 17.9 s = 2651.2 m ahead of the package. This calculation assumes that the plane does not change its velocity or direction during this time, and that air resistance can be neglected.