How High Must the Plane Fly to Drop Supplies Accurately?

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SUMMARY

The problem involves calculating the altitude at which a relief plane must fly to accurately drop a care package into a lake, given a horizontal speed of 59.1 m/s and a drop distance of 521 m. The relevant equation used is yf = yi + Viy*t + 1/2*at^2, where yf is the final vertical position, yi is the initial vertical position, Viy is the initial vertical velocity, and t is the time of flight. Assuming Viy = 0 m/s, the time of flight is calculated to be 8.82 seconds, leading to the conclusion that the plane must be at a specific altitude to ensure the package lands correctly.

PREREQUISITES
  • Understanding of projectile motion principles
  • Familiarity with kinematic equations
  • Basic knowledge of horizontal and vertical motion components
  • Ability to perform algebraic manipulations
NEXT STEPS
  • Calculate the altitude using the derived time of flight and kinematic equations
  • Explore the effects of wind resistance on projectile motion
  • Study real-world applications of projectile motion in aerial supply drops
  • Learn about the physics of inflating rafts upon impact
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Students in physics, engineers involved in logistics and supply chain management, and professionals working in emergency response planning will benefit from this discussion.

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Homework Statement



Need help solving this problem

An emergency relief plane is dropping a care package from a plane to a group of medical personnel working for a relief agency in an African village. The package is designed to land in a small lake, inflate an attached raft upon impact, and finally resurface with the raft side down. The plane will be moving horizontally with a ground speed of 59.1 m/s. The package will be dropped a horizontal distance of 521 m from the intended target location. At what altitude above the pond must the plane be flying in order to successfully accomplish this feat?

yf=0m yi=? Viy=? t=8.82s


Homework Equations


yf=yi+Viyt+1/2at^2

The Attempt at a Solution

Not sure where to go from here
 
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Nm I solved it assuming Viy=0m/s
 

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