Shipment: Drone Delivery Drop

"Drone Delivery Drop!"

A drone is flying horizontally at a steady speed of 12 m/s and drops a package from a height of 60 meters above the ground. The package follows a parabolic path until it lands. You may assume there is no air resistance, and the only force acting on the package is gravity. 

❓Your Task - concrete mathematical thinking:

1. Write an equation that models the height of the package (in meters) as a function of time (in seconds) after it is released. 

hint: you will need to think about what type of equation models falling objects under gravity.

2. Use your equation to determine how long it takes for the package to reach the ground. 

3. How far horizontally does the package travel before it hits the ground?

🔁 Open-ended Questions:

1. If the drone increases its speed to 15 m/s, how would that affect where the package lands? What about changing the release height to 80 m?
   
   

2. What assumptions are you making in your model? How might real-world factors (like wind, package shape, or drone tilt) affect your predictions?
   
   

3. Design a modified drop plan so the package lands on a delivery mat that's only 3 meters wide. What variables can you adjust to make sure it lands accurately? Justify your approach with math.