Centripetal Acceleration with distance

[getty102]

Homework Statement

You plan to throw stones by using a sling of length 0.7 m which you whirl over your head. Suppose you wish to throw a stone a distance of 36 m. What must be the centripetal acceleration of the stone just before its release if it is to reach this distance? Assume that the release height is 3.0 m.

Homework Equations

a_c=v²/r

The Attempt at a Solution

I tried to find the velocity in the x-direction but I didn't have an angle to work with. I then solved x=v₀cosθ(t) for t and plugged that into y=y₀+v₀sinθ(t)-g/2(t)². This gave me -y_o=xtanθ-((gx²)/(2v₀²cos²θ). That didn't cancel anything out.
I'm not sure where to go from there.

 

[PeterO]

Homework Statement

You plan to throw stones by using a sling of length 0.7 m which you whirl over your head. Suppose you wish to throw a stone a distance of 36 m. What must be the centripetal acceleration of the stone just before its release if it is to reach this distance? Assume that the release height is 3.0 m.

Homework Equations

a_c=v²/r

The Attempt at a Solution

I tried to find the velocity in the x-direction but I didn't have an angle to work with. I then solved x=v₀cosθ(t) for t and plugged that into y=y₀+v₀sinθ(t)-g/2(t)². This gave me -y_o=xtanθ-((gx²)/(2v₀²cos²θ). That didn't cancel anything out.
I'm not sure where to go from there.

For this sling, it is the speed of the projectile which determines how far it goes. You will either have to be given or assume an angle of release to find that speed.
Once you know the speed you can calculate the centripetal acceleration.

 

[getty102]

I found time t it takes for the stone to fall 3.0m.

t=√(y_o2/g)

then plugged that t into find the velocity it would take the stone to go 36m.

v_0,x=x/t

I plugged that v, and my r, in v²/r to get my centripetal acceleration although it gave me a too large of number. Where am i going wrong?

 

[PeterO]

I found time t it takes for the stone to fall 3.0m.

t=√(y_o2/g)

then plugged that t into find the velocity it would take the stone to go 36m.

v_0,x=x/t

I plugged that v, and my r, in v²/r to get my centripetal acceleration although it gave me a too large of number. Where am i going wrong?

Show me your numbers. I could work it the way you describe.