Two projectiles, displacement vs. time

[anoorani]

A ball is thrown upward with an initial speed, vo.
When it reaches the top of its flight, at a height h, a second ball is thrown at the same initial velocity.
sketch a displacement vs time graph for both balls.
where do the balls cross from the graph.
Find the height where the paths cross.

answers: above h/2 and 3/4h

please help

 

[phinds]

Well ... draw a graph. You have to show us some work before we know what you are having trouble with.

 

[lep11]

And the title could be more descriptive, too.

Moderator's edit: note, thread title has been changed since this was posted.

 

[anoorani]

This is what I have got...
I am having trouble in the last part..
Though I have got h (max ht) = vo^2/g

 

[Nickie]

I would first like to clarify that this scenario assumes that both balls are thrown in the same direction and at the same angle, with the only difference being that one is thrown after the other at the top of the first ball's flight.

Based on this information, the displacement vs. time graph for both balls would look like two parabolic curves, with the first ball's curve starting at the origin and reaching a maximum height of h before coming back down to the ground, and the second ball's curve starting at the same height and following a similar path.

The balls would cross on the graph at a point above h/2 and 3/4h, as the second ball is thrown at the top of the first ball's flight and therefore reaches its maximum height at the same time as the first ball. This means that at h/2, both balls would have the same displacement and at 3/4h, the second ball would have a displacement of h while the first ball would be on its way back down.

To find the height where the paths cross, we can use the equation for the displacement of a projectile at any given time, which is given by s = ut + 1/2at^2, where s is the displacement, u is the initial velocity, a is the acceleration due to gravity (assuming we are on Earth), and t is time.

Since both balls have the same initial velocity, we can set their equations equal to each other and solve for the time when their displacements will be equal. This will give us the time at which they cross paths on the graph. Then, we can plug this time into either equation to find the displacement at that time, which will give us the height at which the paths cross.

I hope this explanation helps. As a scientist, it is important to carefully analyze and understand the given information before making any conclusions or calculations.