Question

David is riding on a flying carousel which swings him in circles of radius R=4.0R=4.0m, at a height of h=6h=6 m above the ground. The carousel rotates counterclockwise once every 5 sec. When he is on the west side of the carousel, David's hat falls off. Where does the hat land (relative to the point where it fell off)?

Answer 1

hats when it fall off David's head  

it will have only tangential velocity at that time v = R*ω

he carousel rotates counterclockwise once every 5 sec.  

f = 1/5 Hz

ω = 2pi*f = 2pi/5 rad/s

v = R*ω = 4*2pi/5 = 5.02654825 m/s

with this initial speed horizontally hat has to travel 6 m height vertically

in vertical direction  

h = 0+ 1/2*g*t^2

t = sqrt(2h/g) =sqrt( 2*6/9.8) =1.10656667 sec

distance it travelled in this time x = v*t = 5.02654825*1.10656667 =5.56221076 m

answer = 5.56221076 m

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