# Two objects travelling on a parallel plane

by AaronL
Tags: objects, parallel, plane, travelling
 P: 2 Hi, I'm new to this forum, I am currently in grade 12 and I'm desperately (like alot of other students this year) trying to get a good start this year. My physics teacher assigned us a question that I don't quite understand: Two planes are flying over parallel paths. Plane A has an initial speed of 50.0m/s and is accelerating uniformly. Plane B has an initial speed of 120 m/s and an acceleration of 60% of Plane A. If both planes have the samem velocity after travelling the same distance, what is the final velocity of either plane. This question has been bugging me for some time and I need help solving it. my physics is a bit rusty, considering it's been about a year since I last did anything physics related (yikes). If I could get some assistance with this question it would be greatly appreciated. Cheers.
 P: 510 Do you remember the basic kinematics equation for distance as a function of uniform acceleration and initial velocity ?
 PF Patron Sci Advisor Thanks Emeritus P: 38,416 This makes no sense. You started by titling this "Two objects travelling on a parallel plane" but apparently you then came to your senses and realized that you were talking about two parallel planes. Unfortunately, you then said "Plane A has an initial speed of 50.0m/s and is accelerating uniformly. Plane B has an initial speed of 120 m/s and an acceleration of 60% of Plane A". Planes do not accelerate! I am willing to accept that object B accelerates at 60% the acceleration of object A where B and A are objects moving in parallel planes! If A accelerates at "a m/s2", then B accelerates at "0.60a m/s2". You should be able to find the velocity and position of both A and B from v(t)= v0+ at and x(t)= x0+ v0t+ (a/2)t2.
P: 37

## Two objects travelling on a parallel plane

 Quote by HallsofIvy Planes do not accelerate! I am willing to accept that object B accelerates at 60% the acceleration of object A where B and A are objects moving in parallel planes!
i think a plane ( the aircraft ) is an object...
 PF Patron Sci Advisor Thanks Emeritus P: 38,416 OHHH!!! (banging head against computer screen) AIRPLANES!! (You do understand how the phrase "parallel planes" could confuse someone who confuses easily!)
 P: 1,017 That's the funniest thing I've seen on PF in a while. Cheers HoI!
 P: 1,017 Oh yeah, should try and help rather than just laugh at people's misfortune. You need to start by solving t in a simultaneous equation for v = v0 + at for both A and B (i.e. v0A + aAt = v0B + 0.6aAt). Once you've got t you should know where to go next.
 PF Patron Sci Advisor Thanks Emeritus P: 38,416 You're always welcome to laugh at me- I do it all the time!
 P: 193 so can anyone work out the answer and post it here!! i tried it but im not sure if im right
 P: 193 nop i havnt got it didnt work, i must be dumb "grade 12" what age people is it for? im 17 is it something i should worry about not being able to do a question like this being a phys and maths student? reading what u sed i did this 50 + At = 120 + 0.6At - this is saying both their final velocity is the same right? rearanged to 0.4At = 70 then At = 70/0.4 but how do u find t from that?! u got 2 unknown terms so i need another equation to sub into this? i think its better using the equation : root(u^2 + 2as) = root(u^2 + 2as) then could u cancel the distance? from both sides or not cause theres an addition in the equation not just multiples.
 P: 193 ive never seen this x(t)= x0+ v0t+ (a/2)t2. equation before seen one similar x(t)=v0t +(a/2)t2. where did the initial distance come into it.
P: 13
 Quote by alias25 50 + At = 120 + 0.6At - this is saying both their final velocity is the same right? rearanged to 0.4At = 70 then At = 70/0.4 but how do u find t from that?!
you don't need to know t. You know At and that's enough (v=v0+At)
P: 37
 Quote by HallsofIvy You're always welcome to laugh at me- I do it all the time!
Funniest thing in physics i've EVER seen... but i won't laugh at you.... i'd have done the same thing... i just came to MY senses instead of telling him to come to his :P Planes do NOT accelerate... except in the case of aircraft
HW Helper
P: 1,422
 Quote by alias25 nop i havnt got it didnt work, i must be dumb "grade 12" what age people is it for? im 17 is it something i should worry about not being able to do a question like this being a phys and maths student? reading what u sed i did this 50 + At = 120 + 0.6At - this is saying both their final velocity is the same right? rearanged to 0.4At = 70...
Nope. This is not correct.
If you set up an equation like that, you are assuming that two planes have the same final velocity after a specific amount of time, which is not correct.
The problem states that two planes have the same velocity after travelling the same distance. And you don't know how long the distance is.

You know their initial velocity, know that a_2 = 0.6 a_1, d_1 = d_2, and the final velocity of the two planes are the same after travelling the same distance.

So you can use the equation: $$v_f ^ 2 = v_i ^ 2 + 2ad$$ to solve the problem.
Let v_f be both planes' final velocity.
Let d be the distance both planes travel, ie : d = d_1 = d_2
You will have:
$$\left\{ \begin{array}{l}v_f ^ 2 = v_1 ^ 2 + 2a_1 d (1) \\ v_f ^ 2 = v_2 ^ 2 + 2 \times a_2 \times d_2 = v_2 ^ 2 + 2 \times 0.6 \times a_1 \times d = 1.2a_1 d (2) \end{array} \right.$$

Where v_1 is the plane A's initial velocity, v_2 is the plane B's initial velocity. a_1 is the plane A's acceleration, a_2 is the plane B's acceleration.

From the two equations, you will be able to find the final velocity of both planes. First, try to subtract (2) from (1).
Viet Dao,

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