IIT JEE , AIEEE Forum - Physics , Mechanics

srikanth99s

The path of the projectile as seen from another projectile,given u1,u2 and @1,@2 are velocitiesand angles of projections

ksgandharva

Be clear with the question!

mukulss

obviously a st line motion,,,,,,,,,,

think u r on one of the projecttttiles.......

Aatish

Well I also think it will be a straight line motion....as seen by another projectile..

v.sabarish

U need to get the relative motions......

displacement of the first particle, assuming x, y axes, would be
(u1.cos@1.t, u1.sin@1.t-g.t.t/2)
the other one has a similar expression, now subtract the displacements to get the relative displacement.....

you get
t(u1.cos@1-u2.cos@2), t(u1.sin@1-u2.sin@2)
dx/dt as well as dy/dt is a constant... you get a straight line...

shinee

i hav a doubt
suppose if the first projectile has reached its max height(no vertical component of velocity), then at this instant , the path of the other projectile may appear to be a parabola
Is the relative motion always a straight line?

sriram.a

see Shreya the body just cannot stop in the air it moves.this question is totally dependent on relative velocities

shinee

i am speaking abt that particular instant and also one more doubt,
suppose two boys r running in a curved path and also suppose that the curvature of the first guy is more and also irregular, then the second guy can clearly observe that the path of the first guy is curved and not straight
similarly, if the angle is different and the velocities r different, then the path of the first projectile may also look curved as seen 4m the second projectile, can u plz explain this point clearly?
salutes assured

saurabh_reincarnated

@shreya.....

its true that particle movein straigght line.....

bcos u can easily see that in reference frame of one w.r.t. other we have 0 acc. and thus .......

there will be straight line path........ it may be total horizontal or inclined... hoe u understand that.....

now abt that highest point...... how do u decide path by seein the particle at just one moment.........lik can u tell velocity of body at that point if u r gven position of body........

at any moment we only seein body postn cant decide path....

Cheers!!!!!!

v.sabarish

@ above

"bcos u can easily see that in reference frame of one w.r.t. other we have 0 acc. and thus ......."

I guess you should have given more importance to this statement.....
This would most probably be the best explanation than any other......

When both bodies are subjected to the same acceleration, i.e 'g', there is no relative acceleration and the case is identical to one where on observer is at rest and another going with a uniform velocity........
@Shinee
Now tell me, what makes you feel that a body can have a parabolical path when it has uniform velocity.....????

computer001

the relative path is a st line..

srikanth99s

ans isgiven as y/x2= U2sin@2-U!Sin@1/U2cos@2-u1cos@1

shinee

i agree that in the case of 1D motion that if two bodies bodies move with uniform velocity or unifom acceleartion along a straight line , then there is no relative curved path between them
but if we consder the case of uniform motion or uniform acceleration in 2D, then suppose that one body is moving in the xy plane such that it makes an angle of 60 with the x axis and another body makes an angle of 235 with the +ve x axis , then there may be relative curved displament between them
similarly if we consider 3D, then also one body may have some (xi,yj,zk) coordinates and another body may have (pi,qj,rk) cordinates, then also the realtive displacement may be curved

similarly if we consider a projectile (2D), then it may have different curved paths 4 different values of initial velocity and initial angle of projection(like one projectile may be having an initial angle of projecion of 30 with the x axis and another may ahve an initial angle of projection of 178 degree with the positive x axis
i agree that there is no relative curved displacement in the y direction but there is a realtive curved displacement along the x direction, so the resultant would also have a relative curved displacement wrt one another
and also the simialr case can be considered for 3D mtion
how can we say that there is no relative curved motion between two projectiles

uday_zingtudor

Definitely there would be relative curved motion 'coz the times of flight may be different. After one body comes to rest, the other continues its motion which is definitely curved!!

And also if they are projected one along z-axis and the other along x-axis, one wud absolutely find the relative motion to be curved.

If the case is only 2D, then while they are in motion,

horizontal motion:Both of them are moving with constant velocities and so the relative motion is linear

vertical motion : Both of them are movin' under the same accelaration .So in this direction, the relative motion would be linear

Now, when both the horizontal and vertical motion appear to be linear, the resultant motion wud also appear linear!!

~Cheerio!!!

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