1) Yes, your answer is correct. The collision must take place immediately after blocker A leaves the eye of the photogate because this allows the photogate to accurately record the velocity of trolley A before the collision. If the collision were to happen after some time has passed, the recorded velocity would no longer be representative of trolley A's initial velocity.
Additionally, by colliding immediately after blocker A passes through the photogate, blocker A will have more time to gain momentum before the collision. This will result in a larger change in momentum during the collision, providing more accurate data for analysis.
2) Your answer is also correct. Blocker B must enter the eye of the second photogate immediately after the collision because this allows us to measure the velocity of the combined masses (trolley A and B) immediately after the collision. If blocker B entered the eye of the photogate at a later time, the measured velocity would not accurately reflect the post-collision velocity.
By measuring the velocity immediately after the collision, we can determine crucial information such as the conservation of momentum and whether any kinetic energy was lost during the collision. This data can be used to analyze the effectiveness of the collision and gain insights into the physics principles at play.