Medical supplies dropped from a plane (projectile motion)

In summary,The plane is to be used to drop emergency medical supplies to campers in Northern Ontario. The campers are in a clearing. The plane will approach the clearing at an altitude of 150m while flying level at 40m/s.a) The pilot can't drop the supplies until the plane is directly over the campsite.b) The supplies should be dropped 5.5s ahead of the campsite.
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Humbleness
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Homework Statement


A plane is to be used to drop emergency medical supplies (encased in a crash-proof container) to campers in Northern Ontario. The campers are in a clearing. The plane will approach the clearing at an altitude of 150m while flying level at 40m/s.

a) Why can't the pilot wait until the plane is directly over the campsite before dropping the supplies?
b) How far (in meters) ahead of the campsite should the supplies be dropped? Justify your choice.

Homework Equations


Δdv= 1/2 aΔt2 - To find how long until the supplies hit the ground.
horizontal displacement = horizontal velocity which is 40m/s x Δt - To find how far horizontally would the supplies travel after being released from the plane


The Attempt at a Solution


I will first start with b)
So I used the formula:
Δdv = 1/2 aΔt2

150m [down] = 1/2 (9.8m/s2 [down]) Δt2
Δt2 = 150 : 4.9 = √30.6
Δt = 5.5sThen I used the horizontal velocity of 40m/s x 5.5s (the time), to get the answer to horizontal displacement:
40m/s x 5.5s = 220m

So the supplies should be dropped 220m ahead of the campsite. This means that both the plane and the supplies themselves will be at 220m ahead of the campsite at the same time. Am I correct with this part, at least? I would really appreciate a confirmation.

For a) I tried drawing a diagram to show the airplane directly above the campsite, and then tried to draw a triangle, so that perhaps using trigonometry I could find out why the pilot shouldn't drop the supplies when directly above the campsite. But I am still not understanding how to even begin the calculations, using what equation... My main concern is that I am not understanding how to get to the answer to part a. How do I calculate what would happen if the plane dropped the supplies when directly above the campsite? I don't understand.
 
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  • #2
Hi Humbleness and welcome to PF.

Humbleness said:
How do I calculate what would happen if the plane dropped the supplies when directly above the campsite? I don't understand.
You have already calculated that in part (b). When the package is released, it will land 220 m horizontally away from the drop point whether there is a campsite directly below or not. This, of course, assumes your calculation of 220 m is correct.
 
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  • #3
Thank you kuruman for the welcome and quick response! I really appreciate it.
So then, my calculations answered both a and b? I am confused in that case as to how I would vindicate my response to question a. What exactly is it asking of me?
 
  • #4
Humbleness said:

Homework Statement

Then I used the horizontal velocity of 40m/s x 5.5s (the time), to get the answer to horizontal displacement:
40m/s x 5.5s = 220m

So the supplies should be dropped 220m ahead of the campsite. This means that both the plane and the supplies themselves will be at 220m ahead of the campsite at the same time. Am I correct with this part, at least? I would really appreciate a confirmation.

Yes, this is correct, and hence question (a) is answered :) This shows that if you wait for the stuff to be dropped directly above, the supplies will land 220m away from the campsite
 
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Understood clearly now. Thank you so much for helping me clarify the confusion!
 
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FAQ: Medical supplies dropped from a plane (projectile motion)

1. How do medical supplies get dropped from a plane?

Medical supplies are typically dropped from a plane using a method called "airdrop". This involves using a parachute or other method to safely release the supplies from the plane and guide them to the desired location.

2. What is the purpose of dropping medical supplies from a plane?

The purpose of dropping medical supplies from a plane is to provide aid and resources to areas that are difficult to access by ground transportation, such as remote or disaster-stricken areas.

3. How are the supplies packed and organized for a medical supply drop?

The supplies are typically packed into a container or bundle that is specifically designed for airdrops. This may include a parachute or other mechanism to ensure a safe landing. The supplies are also organized and labeled to make it easier for medical personnel to quickly locate and distribute them upon arrival.

4. What factors affect the trajectory and accuracy of the medical supply drop?

The trajectory and accuracy of a medical supply drop can be affected by various factors, such as wind speed and direction, weight and size of the supplies, altitude of the plane, and any obstacles or terrain in the drop zone. These factors must be carefully considered and accounted for to ensure the supplies land in the desired location.

5. What safety precautions are taken during a medical supply drop?

Safety is a top priority during a medical supply drop. Pilots and crew members undergo specialized training to perform airdrops safely and accurately. Additionally, the supplies are carefully packed and inspected to ensure they will not cause harm upon landing. Communication with ground personnel and coordination with air traffic control are also crucial safety measures during a medical supply drop.

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