Naked Science Forum

Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: thedoc on 23/10/2012 16:56:35

Title: What happens when a moving plane drops a parcel?
Post by: thedoc on 23/10/2012 16:56:35

Hi,

I am doing AS level physics and I am stuck on a question. My revision guide has no answers, and it does not explain the topic very well. Could you please help me with it?

The question is:

An aeroplane carrying a parcel drop releases a parcel while travelling at a steady speed of 90ms-1 at an altitude of 200m. Calculate:

a) The time between the parcel leaving the aeroplane and it striking the ground.

b) the horizontal distance travelled by the parcel in this time.

c) The speed at which the parcel strikes the ground.

Any help would be great!

Many thanks,

Tilly Seargeant
Asked by Tilly Seargeant


                                        Visit the webpage for the podcast in which this question is answered. (http://www.thenakedscientists.com/HTML/podcasts/show/20121021/)

 

Title: What happens when a moving plane drops a parcel?
Post by: thedoc on 23/10/2012 16:56:35

We answered this question on the show...



Matt -   You wouldn't be doing the equations of motion for projectiles, would you Tilly?
Tilly -   Yes.
Matt -   Right, so how fast is that package going to fall as you release it?
Tilly -   I don’t know.
Matt -   So, this is the teacher in me.  I try and talk the student through the question!  Initially, it doesn’t matter how fast you're going forward.  If you let go of this package, it’s not going down at all, yet, because gravity hasn't yet kicked in.  And so it’s going to start [with a velocity of] zero.  So, if you put down your starting velocity as zero.  It’s then going to accelerate according to gravity which is about 9.81 meters per second squared.  Do you know which equation you have to use to work out how long it’s going to take to hit the ground?
Tilly -   I'm not sure.  Time taken… so maybe S = ut + ½at²?
Matt -   S = ut + ½at²...  What's the other one?  Is it v²=u²+2as?
Tilly -   Yes.
Matt -   It’s amazing.  These things just get locked in your muscle memory.  So, right what you want to do now is write down...(I feel like I'm just doing tutoring live on the air.  This is great for you and me, Tilly, but everyone else is getting a bit bored.)  You need to write down everything you know.  So you know your starting velocity, you know your acceleration, you know the distance it has to travel, and you want to find out the time.  And so, which of these equations has U and S, and A, and T in it?  That would be the one that you read out to me [S = ut + ½at²].
So now, if you put all your numbers into that equation in theory, so it’s going to be 200²=0(time)+½ at² and acceleration is about 10... So it’s around about… the square root of 8,000 seconds. 
Chris -   So that’s the time to hit the ground for the parcel from that altitude?
Matt -   Yes.
Chris -   So now, we’ve actually got to take into account the movement of the airplane along.
Matt -   So, I'm going to cheat and use a calculator to work out what that will be.  Now, what we should do then is, if you know how fast your plane is going, so it’s going 90… did you say 90 meters per second?
Tilly -   Yeah.
Matt -   So, you multiply – while the parcel is falling, multiply how long it takes to hit the ground by 90 because it’s going to go an extra 90 meters every second and that will give you your grand total which will be around about… 8 kilometres!  There you go.  That’s not bad.
Chris -   There you go, Tilly.  If you get an ‘A’, we want some of the glory, okay?
Tilly -   Yeah.

Title: Re: What happens when a moving plane drops a parcel?
Post by: Phractality on 23/10/2012 18:26:14

The lack of details about the package suggests that you are supposed to ignore the effects of drag and pretend that there is no atmosphere. Therefor, the explanation given on the show is correct. However, this would not work if you were trying to drop the package thru a basketball hoop. Your aim would be pretty close if you are dropping a large lead ball, but a box mostly full of Styrofoam packing bubbles would fall far short of the target and take much longer to hit the ground.

The exact ballistic formula with air drag (http://en.wikipedia.org/wiki/Trajectory_of_a_projectile#Trajectory_of_a_projectile_with_air_resistance) is not a parabolic trajectory. If you are aiming artillery to a target 50 kilometers away, you might even have to consider Earth's rotation and your latitude; then you are calculating a suborbital trajectory with air drag, and the air drag varies with altitude. You just have to decide which parts of the formula are insignificant.

But, as I said, the lack of details about the package suggests that you are supposed to pretend that there is no atmosphere and the Earth is not rotating.