Delievering a package by air. Please help

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In summary, a relief airplane is delivering a food package to a group of people stranded on a small island. The package is dropped from the plane, and it takes approximately 11.1 seconds to reach sea level with an initial horizontal velocity of 290 mph. To land on the island, the package should be released at a horizontal distance of 1430 meters from the plane. The speed at which the package hits the ground can be calculated using the equation vy(t) = v0y + ayt, with the final velocity being the vector sum of the horizontal and vertical components. To decrease the speed and potential damage upon impact, it would be best to decrease the plane's speed and height.
  • #1
physicsgirlie26
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delievering a package by air. Please help!

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 290 mph at an altitude of 600 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 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 = 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 290 mph in the horizontal direction.

I got t=11.1s

If the package is to land right on the island, at what horizontal distance from the plane to the island should the package be released? In meters.

I know i need to use the formula x(t)= x0+v0t but when i plug in the number i get the wrong answer

What is the speed of the package when it hits the ground? In mph.


Please help! Thank you!
 
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  • #2
physicsgirlie26 said:
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 290 mph in the horizontal direction.

I got t=11.1s
OK.

If the package is to land right on the island, at what horizontal distance from the plane to the island should the package be released? In meters.

I know i need to use the formula x(t)= x0+v0t but when i plug in the number i get the wrong answer
What did you plug in? Did you convert the speed to m/s?
 
  • #3
for the second part i got 1430 m

now i just need to find out at what velocity it is hitting the ground in mph.

i have the equation vy(t) =v0y+ayt.

i just don't know what to plug into the equation now.
 
  • #4
The vertical and horizontal components of the velocity can be analysed separately. Assuming negligible friction (air resistance), which would really be unrealistic, but for our purposes... There is no acceleration in the horizontal direction (no force in that direction), so the dropped package has a constant horizontal velocity equal to that of the aeroplane. Distance is time interval multiplied by speed. The time interval is of course that which it takes to fall to sea level.

The speed it reaches upon impact is the magnitude of the vector sum of the horizontal and vertical components of the final velocity of the package. The horizontal component we just discussed, the vertical component is the final velocity after constant acceleration over the time interval you calculated.
 
  • #5
I still don't understand what to do. I mean I get what you are saying but I do not know what numbers to use. This is my first time in a physics class so please bear with me.
 
  • #6
physicsgirlie26 said:
now i just need to find out at what velocity it is hitting the ground in mph.

i have the equation vy(t) =v0y+ayt.

i just don't know what to plug into the equation now.
That's the correct equation for the vertical component of the velocity. You have time and acceleration, so plug away.

Don't forget to find use the horizontal and vertical components to calculate the magnitude of the total velocity at impact.
 
  • #7
so its vy(t)= 0 +9.8(11.1)?
 
  • #8
physicsgirlie26 said:
so its vy(t)= 0 +9.8(11.1)?
Yep.
 
  • #9
Thank you! i got it
 
  • #10
The speed at which the package hits the ground is really fast! If a package hits the ground at such a speed, it can be crushed and also cause some serious damage on the ground. Which of the following would help decrease the speed with which the package hits the ground?

Increase the plane's speed and height?

Decrease the plane's speed and height?
 
  • #11
This one shouldn't require any calculation. :wink:
 
  • #12
hahaha yeah i got it yesterday. Thanks for all of your help! :smile:
 

1. How do packages get delivered by air?

Packages are delivered by air through the use of airplanes or drones. The package is loaded onto the aircraft, which then travels to the designated location for delivery.

2. What are the advantages of delivering packages by air?

The main advantage of delivering packages by air is speed. Air transportation is much faster than ground transportation, allowing packages to reach their destination in a shorter amount of time. Additionally, air delivery can access remote or hard-to-reach areas more easily.

3. Are there any risks involved with delivering packages by air?

As with any form of transportation, there are potential risks involved with delivering packages by air. These risks include weather conditions, mechanical malfunctions, and human error. However, strict safety protocols are in place to minimize these risks.

4. How is the weight and size of a package determined for air delivery?

The weight and size of a package are determined by using a combination of factors such as the dimensions, density, and weight. This information is then used to calculate the cost of shipping and determine the appropriate aircraft for transportation.

5. What happens if a package is lost during air delivery?

In the rare event that a package is lost during air delivery, the delivery company will conduct a thorough investigation to locate the package. If the package cannot be found, the delivery company will provide compensation to the sender or recipient, depending on the terms of the shipping agreement.

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