Back in the day Carowinds had a ride called the Oaken Bucket (closed in 1987). My first attempt to ride ended in disappointment; however, when I returned a few months later, my courage was at the sticking-place, willing to give the ride another try. We were led into a circular room with about 20 other people and we stood with our backs against the wall; they closed the door. When the time came, the room would spin; the floor would drop and we would feel pinned against the wall; presumably not falling. I decided I was going to toss a 0.3 kg ball from my position to the spot on the other side of the room. I estimated the distance from my position to the spot on the other side would be 12.6 m. I would toss the ball horizontally from a distance of 1.70 m above the bottom of my feet; and my friend would catch it on the other side at a distance of 1.20 m above the bottom of my feet.
How much time would the ball be in flight?
What would the initial speed of the ball be?
What is the velocity of the ball when it is caught?
If I am going to catch the ball on the opposite side of the circle, what does the angular speed of the room need to be?
At this angular speed, what is my linear speed?
Before we started to move, I noticed a stain on the ceiling right above me. Once we started to spin, I felt myself tangentially accelerating to my right. Once we reached a constant angular velocity, I noticed that it took 2.1 seconds to go around once. At what angle would I need to throw the ball (with respect to me) in order to catch the ball on the directly opposite side of the room, where the directly opposite side is defined from the moment I release the ball, assuming that I throw the ball when the room is at maximum velocity?