A 7 x 10^-3kg bullet is fired into a 2kg wooden block initially at rest on a level surface. The bullet passes through the block and emerges with the velocity of 200m/s. The block slides 0.5m and stops. If the coefficient of friction between the block and the surface is 0.3, find a) the initial velocity of the bullet, b) the velocity of the block right after being hit by the bullet, and c) the energy loss of the bullet during the collision

(b) Use the stopping distance of the block, X, to get its velocity after the bullet goes through, Vblock.

(1/2)M*Vblock^2 = M*Uk*g*X

(a) The momentum loss of the bullet equals the momentum gain of the block. Use that fact to calculate the initial bullet velocity, Vi.

(c) Bullet energy loss =
(1/2)Mbullet*(Vi^2 - 200^2)

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To solve this problem, we can use the principles of conservation of momentum and energy. Let's break down the steps to find the answers to the three questions:

a) To find the initial velocity of the bullet, we need to consider the conservation of momentum before and after the collision. The total momentum before the collision should be equal to the total momentum after the collision. We can express this as:

(Mass of bullet * Initial velocity of bullet) = (Mass of bullet * Final velocity of bullet) + (Mass of block * Final velocity of block)

Let's plug in the values we have:
(7 x 10^-3kg * Initial velocity of bullet) = (7 x 10^-3kg * 200m/s) + (2kg * Final velocity of block)

Since the block is initially at rest, we know its final velocity is zero:
(7 x 10^-3kg * Initial velocity of bullet) = (7 x 10^-3kg * 200m/s) + (2kg * 0)

Simplify the equation:
(7 x 10^-3kg * Initial velocity of bullet) = 1.4kg m/s

Now, divide both sides of the equation by (7 x 10^-3kg) to solve for the initial velocity of the bullet.

b) To find the velocity of the block right after being hit by the bullet, we also need to consider the conservation of momentum. Since the block stops after sliding 0.5m, we can use the equation:

(Mass of bullet * Final velocity of bullet) + (Mass of block * Initial velocity of block) = 0

Plugging in the values we have:
(7 x 10^-3kg * 200m/s) + (2kg * Initial velocity of block) = 0

Simplify the equation:
(1.4kg m/s) + (2kg * Initial velocity of block) = 0

Now, solve for the initial velocity of the block.

c) To find the energy loss of the bullet during the collision, we can use the principle of kinetic energy conservation. The initial kinetic energy of the bullet is given by:

Initial kinetic energy of bullet = 0.5 * (Mass of bullet) * (Initial velocity of bullet)^2

The final kinetic energy of the bullet is given by:

Final kinetic energy of bullet = 0.5 * (Mass of bullet) * (Final velocity of bullet)^2

The energy loss can be calculated as:

Energy loss = Initial kinetic energy of bullet - Final kinetic energy of bullet

Plug in the known values and solve for the energy loss of the bullet.