Back in the day, Carowinds had a ride called the Oaken Bucket (closed in 1987).
ID: 1531064 • Letter: B
Question
Back in the day, Carowinds had a ride called the Oaken Bucket (closed in 1987). My first attempt to ride it ended in disappointment. However, a few months later, I returned, screwing my courage to the sticking-place, willing to give the ride another try. When it came time, I was led into a circular room with about 20 other people; 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. [People wearing classic 70s polyester would slide down inside their clothes.]
I decided I was going to toss a 0.3 kg ball to myself while riding around the bucket. I first estimated the distance from my position to the spot on the other side of the room to be 12.6 m away. I would toss the ball horizontally from a distance of 1.70 m above the bottom of my feet, and I would catch it on the other side at a distance 1 m above the bottom of my feet.
a) How much time would the ball be in flight?
b) What would the initial speed of the ball be?
c) What is the velocity of the ball when it is caught?
d) 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?
e) At this angular speed, what is my linear speed?
Before we started to move, I noticed a stain on the ceiling right above me. The walls and floor (but not the ceiling) started to spin; I felt myself tangentially accelerating to my right. Once we reached a constant angular velocity, I noticed that it took 5.21 seconds to go around once (using the spot as motionless point).
f) 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 angular speed?
Assume that a line from the me to the center of the room defines 0 degrees. I am at the vertex Use standard convention: counter-clockwise angles are positive.
Explanation / Answer
(a) time t = squar root (2*H/g)
H = 1.70-1.00
= 0.70 m
t = squroot (2*0.7/9.8)
= 0.143 sec
(b)the initial speed of the ball v
v = x/t
= 12.6 m/0.143 sec
= 88.11 m/sec
(c)the velocity of the ball when it is caught vf
vf = squar root (v^2 + 2*g*H^1/2*2)
= squar root (88.11^2 + 2*9.8*0.70)
= 88.18 m/s
(d)angular speed of the room w
w*t = pi
w = pi/ 0.143
= 21.969 rad/sec
(e)linear speed v
v = 2 * w
= 2 * 21.969
= 43.938 rad/sec
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