A ballistic pendulum, as shown, is a system which can be used to measure the speed of a projectile.

If
\(m_{b}=10.0 \text{ g}\) (the mass of the bullet),

\(m_{w}=4.00\text{ kg}\) (the mass of the weight),

and \(y=4.00\text{ cm}\) (the maximum height of block's swing),

find \(v_{1}\), the initial velocity of the bullet in meters per second.

**Details and Assumptions**

- Take \(g\) as \(9.81 \text{ms}^{-2}\).
- Give your answer to 3 significant figures.

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