physics
posted by natalie .
As some molten metal splashes, one droplet flies off to the east with initial speed vi at angle θi above the horizontal, and another droplet flies off to the west with the same speed at the same angle above the horizontal, as inthe figure. In terms of vi and θi, find the distance between the droplets as a function of time. (Use v_i for vi, q_i for θi, and t as appropriate in your equation for the distance.)

Both droplets initially rise and then fall due to gravity. Both droplets have the same altitude at a given time, because they started with the same angle (from horizontal) and speed. Therefore the distance between them is determined by their horizontal coordinate along the eastwest axis only. That is proportional to the horizontal component of the initial velocity. The separation is double the distance that either one travels hotizontally, because they go in opposite directions.
The separation is therefore
2 (v_i)cos(q_i)t