Calculating Impact Speed of a Wrecking Ball: A Quick Energy Question

[ProBasket]

a wreacking ball is used to demolish a building. The 600-kg ball starts from rest, with it's 37-m-long cable making a 22 degrees angle with the vertical. it strikes the building when the cable is vertical. What is the speed of the ball on impact?

it doesn't seem like a hard question, but i can't figure it out.

$$U_o =mgL(1-cos(\theta))$$
$$K_0 = 0$$

$$U_f = 0$$
$$K_f = 1/2mv^2$$

$$mgL(1-cos(\theta)) = 1/2mv^2$$
$$V= \sqrt{\frac{gL(1-cos(\theta))}{2}}$$

plugging in known values, i get 3.6 but the book gets 7.3 m/s. am i missing something?

 

[xanthym]

a wreacking ball is used to demolish a building. The 600-kg ball starts from rest, with it's 37-m-long cable making a 22 degrees angle with the vertical. it strikes the building when the cable is vertical. What is the speed of the ball on impact?

it doesn't seem like a hard question, but i can't figure it out.

$$U_o =mgL(1-cos(\theta))$$
$$K_0 = 0$$

$$U_f = 0$$
$$K_f = 1/2mv^2$$

$$mgL(1-cos(\theta)) = 1/2mv^2$$
$$V= \sqrt{\frac{gL(1-cos(\theta))}{2}}$$

plugging in known values, i get 3.6 but the book gets 7.3 m/s. am i missing something?

Your final equation should be:

$$\blacktriangleright \blacktriangleright \ \ \ \ \color{red} v \ = \ \sqrt{2gL(1 - \cos(\theta))}$$

Use this correct version, and you'll obtain the book answer.


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[ProBasket]

oops your right, thanks for the help