Equations of motion ( vectors )

[sambarbarian]

Homework Statement

Two particles move near the surface of the Earth with u. acc 10 m/s^2 towards the ground . At the initial moment , the particles were located at one point in space and moved with velocities 3m/s and 4 m/s in opposite directions . Find the distance between the particles when their velocity vectors are mutually perpendicular .

Homework Equations

s = ut + 1/2 at^2

The Attempt at a Solution

the trajectory of the particles should form a half - ellipse .

That's as far as i got , how should i relate the mutually perpendicular thing ??

 

[mfb]

the trajectory of the particles should form a half - ellipse .

No.
You can work with a homogeneous gravitational field here (same 10m/s^2 downwards everywhere). How do the paths look like? Can you write them as vectors?

 

[sambarbarian]

As they have the same origin and are moving in opposite directions , while one's velocity is greater under uniform gravitation , Their paths together should form a half ellipse . :/

 

[mfb]

How does the path of the first object look like?
How does the path of the second object look like?

There is no way to combine them to a part of an ellipse, even if an ellipse can look a bit similar.

 

[sambarbarian]

so it will not form an ellipse , how should i solve this ?

 

[mfb]

With the hints I gave in my posts?

After time t, what are the horizontal and vertical velocities of the objects?
What does "orthogonal" mean for vectors?

 

[Saketh#]

Since there is no force in the horizontal direction,velocity changes only in the vertical direction.Assume after some time t they(velocity vectors) subtend some angles(α and β) with the horizontal.Since both the vectors should be perpendicular,derive a relation and solve.

Hope this hepls