S.I.N. 72 Question - Angular Velocity?

[Suck at This]

Question: An Australian bushman hunts kangaroos with the following weapon, a heavy rock tied to one end of a light vine of length 2.0m. He holds the other end above his head, a point 2.0m above the ground level, and swings the rock in a horizontal circle. The cunning kangaroo has observed that the vine always breaks when the angle measure between the vine and the vertical reaches 60 degrees. At what minimum distance from the hunter can the kangaroo stand with no danger of a direct hit?

I used v=$$\sqrt{2gR(1-cos\theta)}$$ and got a velocity of 4.4
I don't know where to go from there.

Any help would be appreciated.

 

[Chi Meson]

It's a projectile motion problem from there. Considering the distance above ground as being 2m-2cos60°, and the initial velocity is completely horizontal.

 

[thomate1]

I can provide some insight into this question. The formula you have used, v=\sqrt{2gR(1-cos\theta)}, is correct and relates the angular velocity (v) of the rock to the gravitational acceleration (g), the radius of the circle (R), and the angle between the vine and the vertical (θ). However, in order to determine the minimum distance the kangaroo should stand from the hunter, we also need to consider the speed at which the rock is being swung and the time it takes for the vine to break.

First, let's find the speed of the rock. We can use the formula for linear velocity, v=ωR, where ω is the angular velocity (v) and R is the radius of the circle. Since the length of the vine is 2.0m and the rock is being swung in a horizontal circle, the radius of the circle is also 2.0m. Substituting this into the formula, we get v=ω(2.0m). Since we know the angular velocity (v=4.4), we can solve for the linear velocity, which is 8.8 m/s.

Now, we can use the formula for time, t=2π/ω, to find the time it takes for the vine to break. Substituting the angular velocity (v=4.4) into this formula, we get t=2π/4.4, which is approximately 1.43 seconds.

Finally, we can use the formula for distance, d=vt, to find the minimum distance the kangaroo should stand from the hunter. Substituting the linear velocity (v=8.8 m/s) and the time (t=1.43 seconds) into this formula, we get d=(8.8 m/s)(1.43 seconds), which is approximately 12.6 meters.

Therefore, the kangaroo should stand at least 12.6 meters away from the hunter to avoid being hit by the rock. However, it is important to note that this calculation assumes ideal conditions and does not take into account factors such as wind resistance or the strength of the vine. The hunter and kangaroo should both exercise caution and use their own judgment in this situation.