Using your understanding of kinematic equations and the given variables in the scenario, calculate the horizontal and vertical motion of the payload to ensure it arrives at the drop site. In your calculations, account for both the horizontal and vertical motion of the payload. Your calculations should address the following:

Initial velocity of the payload when launched

The velocity of the payload when it hits the ground

Following your calculations, describe the equations used in calculating the vertical and horizontal motion of an object. In your descriptions, address the following:

What is the relationship between vertical and horizontal motion in kinematics equations?

How did you analyze the vertical motion of the payload in your solution?

How did you analyze the horizontal motion of the payload in your solution?

What other kinematics principles did you consider in analyzing the motion of the payload?

Following your initial calculations, your supervisor has asked you to consider two additional scenarios. For both scenarios listed below, adapt your diagrams and descriptions to respond to changing variables. Create a diagram describing the horizontal and vertical motion of the payload in order to reach the drop site, and then use your understanding of kinematic equations to describe how these changes would affect calculations for the payload. The two additional scenarios are described below:

In order to prepare pilots for changes in condition, you have been asked to model supply drops by a plane flying into a headwind. For this scenario, you will choose your own location. Use a resource such as the National Weather Service to select a location. Be sure to name the location and use the wind speed in the area to determine the headwind for the plane. For this scenario, consider the plane$$s speed and the height above the drop site to be the same as the first scenario: a speed of $250$ miles per hour relative to the ground and at a height of $2,650$ meters above the target site.

Due to historical difficulty in delivering supplies by plane, one of your colleagues has suggested you develop a catapult for slinging supplies to affected areas, similar to the electromagnetic lift catapults used to launch planes from aircraft carriers. This catapult is located at a fixed point $400$ meters away and $50$ meters below the target site. The catapult is capable of launching the payload at $67$ meters per second and an initial launch angle of $50$ degrees. Using your knowledge of kinematics equations, determine whether this would be sufficient to deliver the payload to the drop site.

Once you have completed your adjusted diagrams and equations, describe the effects of changing variables on kinematic equations. These descriptions should reflect the different motions and considerations made for the modifications you considered in the previous step. In your descriptions, be sure to address the following:

How did the changing variables affect the vertical and horizontal motion of the payload?

What adjustments to delivery would need to be made to account for these changing variables?