How Far Does the Ball Land from the Pole?

[Eitan Levy]

Homework Statement

l=2m
b=1.5m
The mass of the chair is 5kg.
A boy with a mass of 50kg sits on the chair.
The distance of the chair from the pole is 3m, and it spins around it horizontally with a radial velocity of 1.95 rad/s.
The boy drops a ball at some moment, what would be its distance from the pole when it hits the ground if the distance of the chair from the ground when it doesn't spin is 0.5m?

Homework Equations

The Attempt at a Solution

First I drew this:

ω²r=v²/r
v=5.85m/s (The velocity of the ball when the boy drops it, all of it horizontal.
Then -1.177=-5t² (The times it will take the ball to hit the ground).
t=0.4851
Δx=vt=2.8378m
Total distance from the pole: √(3^2+2.8378^2)=4.13m
The answer in the book is 12.42m, I have no idea how they could possible reach to such a large distance.

 

[kuruman]

Can you show in detail how you got the initial velocity, 5.85 m/s? It doesn't match the numbers in your figure.

 

[Eitan Levy]

Can you show in detail how you got the initial velocity, 5.85 m/s? It doesn't match the numbers in your figure.

It says that the TOTAL distance of the chair from the pole while it spins at this radial velocity is 3m. Therefore r=3m.

 

[kuruman]

I see. OK, I cannot find anything wrong with your answer. One could get an answer close to the one in the book if one used ω²r for v instead of ωr.

 

[Eitan Levy]

I see. OK, I cannot find anything wrong with your answer. One could get an answer close to the one in the book if one used ω²r for v instead of ωr.

Alright, thank you!