A hot air balloon competition requires a balloonist to drop a ribbon onto a target on the ground. Initially the hot air balloon is 50 meters above the ground and 100 meters from the target. The wind is blowing the balloon at v = 15 meters/sec on a course to travel directly over the target. The ribbon is heavy enough that any effects of the air slowing the vertical velocity of the ribbon are negligible. How long should the balloonist wait to drop the ribbon so that it will hit the target? time =

The waiting time is  

Explanation:

From the question we are told that

       The  height of the hot air balloon above the ground is  

         The distance of the balloon from the target is  

        The  velocity of the balloon is  

Generally the time it will take to reach the ground  is

substituting values

The distance that is covered at time with the given velocity is mathematically evaluated as  

substituting values

This implies that for the balloon moving at a velocity (v) to hit the target  it must be dropped at this distance (z)

Now the distance the balloonist has to wait before dropping in order to hit the target is  

substituting values

This implies that the time the balloonist has to wait is  

substituting values