How Far Does a Package Travel Horizontally When Dropped from a Plane?

[yoyophysics1]

Homework Statement

An Alaskan rescue plane drops a package of emergency rations to a stranded party of explorers. The plane is traveling horizontally at 100 m/s at a height of 50 m above the ground. What horizontal distance does the package travel before striking the ground? what is the veloicty of the package before it hits the ground?

Homework Equations

X=Vox(t)
Y=Yo+Voy(t)+1/2G(t)^2

The Attempt at a Solution

I found the x and y components but could not find time and further on. Any help is appreciated.

 

[srmeier]

Let me ask you this:

when the package initial leaves the plane, what is it's y-component of velocity? Also, as the package travels towards the ground, does the x-component vary at all?

(side note: I am assume we are ignoring air resistance?)

 

[yoyophysics1]

Let me ask you this:

when the package initial leaves the plane, what is it's y-component of velocity? Also, as the package travels towards the ground, does the x-component vary at all?

(side note: I am assume we are ignoring air resistance?)

for the y component i got 44.8 and x component i got 89.4. I don't quite understand what you mean when you ask if the x component varies.

and yes, ignore air resistance. I am in my first year of physics so I am sure the problems can't be too complex for you guys.

 

[ideasrule]

for the y component i got 44.8 and x component i got 89.4. I don't quite understand what you mean when you ask if the x component varies.

How did you get those values? Are you sure the y component is 44.8 when the package leaves the plane?

Asking why the x component varies is the same as asking whether the package's horizontal speed changes. Does it?

 

[yoyophysics1]

For the x component I used the equation: Vox=VoCOS(theta)

Um I would guess that the horizontal speed doesn't change because velocity is constant in the x direction?

sorry I am a complete newbie to physics and I am trying to study for a test that I am not completely ready for at the moment

 

[ideasrule]

For the x component I used the equation: Vox=VoCOS(theta)

Um I would guess that the horizontal speed doesn't change because velocity is constant in the x direction?

How did you get V0 or theta?

The package's horizontal speed is 100 m/s when it was dropped from the plane, so it follows that it must be 100 m/s throughout the package's flight.

 

[yoyophysics1]

No, I don't know what you mean by the intial velocity vector. I've never heard of it before :/.

I think the package is traveling faster in the x direction because wouldn't it have an initial velocity of 100 m/s?

 

[yoyophysics1]

I got theta by using tan^-1(50/100)

did i at least do that right?

 

[srmeier]

I got theta by using tan^-1(50/100)

did i at least do that right?

well, think about that...

theta is in radians (or degrees), 50[m]/100[m/s] give you units of seconds.

 

[yoyophysics1]

Oh I see.

So I guess my question is how do I find the x and y components correctly because I obviously did them wrong the first time. When I find the x and y components then I can find theta using inverse tan, correct?

 

[srmeier]

I am going to state some of what is known, think about these quantities/ideas.

1) the x-component is constant because there isn't an acceleration in the x-direction.
2) the initial y-component is zero because that is how the problem is defined.
3) the package accelerates in the y-direction, this is due to gravity.

How can we use some of this?

(trigonometry isn't apart of this problem)

 

[yoyophysics1]

Oh, I finally got it! those last three ideas really helped. i didn't realize that the initial y-component was supposed to be zero. Thanks a lot srmeier!

 

[srmeier]

Oh, I finally got it! those last three ideas really helped. i didn't realize that the initial y-component was supposed to be zero. Thanks a lot srmeier!

My pleasure, I must sleep now ^^

as you continue your journey remember these things (and think about why I would tell you them):
1) the time in which it takes the object to travel form 50m to 0m in the y-direction is equal to the time in which the object travels horizontally in the x-direction.
2) to solve a quadratic equation google: the quadratic formula. (because the initial y-velocity is zero you don't need this formula but it may come up on your test)
3) to find a resultant vector given its components use the Pythagorean theorem.

If these hints confuse you at first that is ok. Take things one step at a time.