To summarize:
a) The two masses are initially 30 meters apart. After 0.5 seconds, the mass thrown upwards will have reached a height of 15 meters (since it is moving against gravity at a constant speed). Therefore, the distance apart is 30 - 15 = 15 meters.
b) To determine if the masses will meet, we need to calculate the time at which they will be at the same height. We can set the distance apart equation equal to zero and solve for time:
distance apart = 30 - 15t
0 = 30 - 15t
15t = 30
t = 2 seconds
Next, we need to determine the velocity of the thrown mass at t = 2 seconds. Using the equation v = initial velocity + g * time, we get:
v = 15 - 9.8 * 2
v = -4.6
Since the velocity is negative, it means the mass is descending. Therefore, the two masses will meet when the thrown mass is descending (falling back down) and the dropped mass is also falling.
In conclusion, the masses will meet when one is falling and the other is also falling.