Calculating Particle Collision Time and Speeds in Vertical Projection

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In summary, the two particles will collide when they are at the same height and the time elapses before the collision is 2u/g.
  • #1
Jess1986
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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 particles will collide when they are at equal height. I've started by finding the distance formula for particle 1 but am unsure how i should use T in an equation for particle 2??
 
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  • #2
try drawing a graph of height as a function of time for both particles.
(time is the horizontal axis, height is the vercital axis)
since there are no other forces at play here (besides gravitation) then you can draw the movement of particle1 as a parabula. the same goes for particle2.
after you've done this you should be able to figure out where to go from there.

if you're having trouble understanding me please let me know and i'll try adding a sketch.
 
  • #3
ive made a sketch and it is clear of the point when the particles collide. I have not solved these type of problems using graphs before. How do i go about finding the time of collision?
 
  • #4
i believe it's always better to visualize the problem.
the particle movement is identical. everything is the same except for the time of launch.
let's call:
T0 = time of launching particle1.
gap = the gap between the launches.
T1 = time of collision.
so on the equation of particle2 just place (T-gap) instead of T.
**note the negative sign
you should be able to continue from there.
 
  • #5
the equations i have are for the distance traveled by the particles and not the height reached. As the particles will have traveled different distances when they reach the same height this will not work. How do i find equations for height?
 

What is a particle projected vertically?

A particle projected vertically refers to a physical object or substance that is launched or thrown into the air in a straight upward direction.

What is the purpose of projecting particles vertically?

The purpose of projecting particles vertically is to study the effects of gravity and air resistance on the motion of objects, as well as to collect data and information on the properties of the particles themselves.

What factors affect the trajectory of a particle projected vertically?

The trajectory of a particle projected vertically is affected by several factors, including the initial velocity and angle of projection, air resistance, and the strength of gravity. Other factors such as wind and temperature can also play a role in the particle's trajectory.

How is the motion of a particle projected vertically calculated?

The motion of a particle projected vertically is calculated using the principles of projectile motion, which take into account the particle's initial velocity, angle of projection, and the forces acting upon it, such as gravity and air resistance. Mathematical equations, such as the kinematic equations, can be used to calculate the particle's position, velocity, and acceleration at any given time.

What are some real-world applications of studying particles projected vertically?

Studying particles projected vertically can have various real-world applications in fields such as physics, engineering, and sports. For example, understanding the motion of a baseball when it is thrown can help baseball players improve their pitching skills. In engineering, this knowledge can be applied to design and test projectiles such as rockets or missiles. Additionally, studying particle motion can provide insights into the behavior of fluids and gases, which can have applications in industries such as aviation and meteorology.

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