Calculating Time Between Two Projectile Collisions

[sara_87]

Homework Statement

At time t1, the boy throws a ball at an angle theta1
After some time (say t2), the boy throws another ball at an angle theta2
The initial velocity for both balls is the same (say v0)
The balls collide at B, a distance of y (as shown in the attachment)
the veritcal velocity at B is unknown
The question is:
Find the time between when the 2 balls were thrown.

Homework Equations

horizontally: the velocity stays the same, the distance is x, there is no acceleration.
vertically: the acceleration is g (under free gravity)

The Attempt at a Solution

Horizontally:
first ball: x = v0cos(theta1)t1 (using the equation s = ut + 1/2 at^2)
second ball: x = vocos(theta2)t2

vertically:
first ball: y = v0sin(theta1)t1 + 1/2 g(t1)^2
second ball: y = v0sin(theta2)t2 + 1/2 g(t2)^2

I tried to make t1 the subject from the horizontal equations but after substituting them into the vertical equations, i found it difficult to make t2 the subject (if it is even possible).
so, maybe there is another approach.

Any help is very much appreciated.
Thank you.

 

[micromass]

I suggest posting this in the physics forum...