Final answer:
To determine when two balls thrown vertically will meet, kinematic equations are solved to find the time where their positions coincide. Displacement equations for each ball are set equal to each other and solved for time, taking into account the 2-second delay between the throws.
Step-by-step explanation:
The question involves solving for the time at which ball A and ball B will meet after being thrown vertically upwards and downwards, respectively. To find the answer, we apply the principles of kinematics in one dimension. Ball A is thrown upwards with velocity u, and after 2 seconds, ball B is thrown downwards with a speed 2u. We need to establish equations for the vertical motion of both balls and solve for the time at which their positions coincide.
We know that the displacement s for ball A after time t+2 seconds (since it is thrown 2 seconds earlier) can be described by the equation s = ut - (1/2)gt^2, where g is acceleration due to gravity. Similarly, the displacement for ball B thrown downwards with velocity 2u after t seconds can be given by s = 2ut + (1/2)gt^2. Setting these displacements equal and solving for t, we find the time at which both balls meet. This involves algebraic manipulation and potentially solving a quadratic equation.