Solving for Time of Collision for 2 Particles with Initial Speed u

In summary, the conversation involves finding the time and speed at which two particles, projected vertically with the same initial speed and time interval between projections, will collide. The formula for distance traveled is found to not be applicable, so the suggestion to equate the equations for both particles is given. Time is taken as t for the first projection and t-T for the second projection, and t is solved in terms of T.
  • #1
Jess1986
43
0
This is a follow from a post i made yesterday. The question is:

2 particles are projected vertically up one after another from the same point at same initial speed u. T is the time interval between the 2 projections, where T<2u/g. Find what further time elapses before the particles collide, and find their speeds immediately before impact.

The equations i have found so far are for distance traveled
x= -0.5gt^2 + ut.
However i have realized this formula is for the distance the particle has traveled rather then the height reached. Since i need to find the time when the particles will collide (ie when they are at the same height) i am stuck as i think the formula is no use?! Please help
 
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  • #2
Hint : x is not actual distance but displacement.
Can u go from here?
 
  • #3
so i should equate the equations for x for both particles? how would i substitute T into the equation for particle 2?
 
  • #4
Yes u should equate x.

Take t as time for first proj. and t-T for second proj.
Solve for t in terms of T.
 
  • #5
ok that's great thanks for your helpx
 

FAQ: Solving for Time of Collision for 2 Particles with Initial Speed u

What is the equation used to solve for time of collision for 2 particles with initial speed u?

The equation used to solve for time of collision for 2 particles with initial speed u is t = (2d)/(u1+u2), where d is the distance between the particles and u1 and u2 are the initial speeds of the particles.

How is the distance between the particles calculated?

The distance between the particles is calculated using the equation d = ut + (1/2)at2, where u is the initial speed, a is the acceleration, and t is the time elapsed.

Can this equation be used for particles with different initial speeds?

Yes, this equation can be used for particles with different initial speeds. The initial speeds of both particles are taken into account in the equation, making it applicable for any two particles with initial speeds u1 and u2.

What happens if the particles have the same initial speed?

If the particles have the same initial speed, the time of collision will be infinite. This means that the particles will never collide, as they will always remain at the same distance from each other.

What other factors can affect the time of collision between two particles?

Other factors that can affect the time of collision between two particles include changes in initial speed, changes in acceleration, and the presence of external forces such as friction or air resistance. Additionally, the shape and size of the particles can also impact the time of collision.

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