Calculating Package Delivery by Air: Time, Distance, and Velocity

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SUMMARY

The discussion focuses on calculating the time, distance, and velocity involved in delivering a package by air to a small island. The airplane maintains a constant horizontal speed of 200 mph at an altitude of 850 m. The time taken for the package to reach sea level after being ejected is determined by the vertical motion, which is influenced by gravity (g = 9.80 m/s²). Additionally, the horizontal distance D from the plane to the island for optimal package landing is calculated based on the time of fall.

PREREQUISITES
  • Understanding of projectile motion principles
  • Basic knowledge of kinematics equations
  • Familiarity with gravitational acceleration (g = 9.80 m/s²)
  • Ability to perform calculations involving horizontal and vertical motion
NEXT STEPS
  • Calculate the time of fall using the equation for vertical motion
  • Determine the horizontal distance D using the time of fall and horizontal speed
  • Analyze the final velocity of the package upon impact with the ground
  • Explore real-world applications of projectile motion in delivery systems
USEFUL FOR

Students studying physics, aerospace engineers, and professionals involved in logistics and delivery systems will benefit from this discussion.

markiii
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A relief airplane is delivering a food package to a group of people stranded on a very small island. The island is too small for the plane to land on, and the only way to deliver the package is by dropping it. The airplane flies horizontally with constant speed of 200 mph at an altitude of 850 m . The positive x and y directions are defined in the figure. For all parts, assume that the "island" refers to the point at a distance D from the point at which the package is released, as shown in the figure. Ignore the height of this point above sea level. Assume that the acceleration due to gravity is g = 9.80 .m/s^2
After a package is ejected from the plane, how long will it take for it to reach sea level from the time it is ejected? Assume that the package, like the plane, has an initial velocity of 200 in the horizontal direction.
If the package is to land right on the island, at what horizontal distance D from the plane to the island should the package be released?
What is the speed v_f of the package when it hits the ground
 
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i need help bad I'm so confused
 
do the vertical motion first, because the altitude sets the time of fall.

you DO know how far it falls, right?
do you know how to write that vertical location as a function of time?
You realize that the vertical speed starts out as zero?
 

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