How Do You Calculate the Release Point for an Air-Dropped Package?

[physicsgirlie26]

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!

 

[Doc Al]

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?

 

[physicsgirlie26]

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.

 

[bel]

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.

 

[physicsgirlie26]

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.

 

[Doc Al]

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.

 

[physicsgirlie26]

so its vy(t)= 0 +9.8(11.1)?

 

[Doc Al]

so its vy(t)= 0 +9.8(11.1)?

Yep.

 

[physicsgirlie26]

Thank you! i got it

 

[physicsgirlie26]

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?

 

[Doc Al]

This one shouldn't require any calculation.

 

[physicsgirlie26]

hahaha yeah i got it yesterday. Thanks for all of your help!