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Forensic scientists can measure the muzzle velocity of a gun by firing a bullet horizontally into a large hanging block that absorbs the bullet and swings upward. (See (Figure 1).) The measured maximum angle of swing can be used to calculate the speed of the bullet. In one such test, a rifle fired a 4.20 g bullet into a 2.50 kg block hanging by a thin wire 75.0 cm long, causing the block to swing upward to a maximum angle of 32.6 ∘ from the vertical.

What was the original speed of this bullet?

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Step 1

By conservation of momentum, the momentum of the bullet before collision is equal to the momentum of the bullet and block after collision.

Step 2

By the conservation of the energy, the kinetic energy of the bullet and the block at lowest point is equal to the sum of the potential energy of the block and the bullet at the highest point.

Step 3

The free body di...

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