a 35 kg bullet moving at 475 m/s. strikes a 2.5 kg wooden block. the bullet passes through the block, leaving at 275 m/s. the block was at rest when it was hit. how fast is it moving when the bullet leaves?
2.8
To determine how fast the block is moving when the bullet leaves, we need to apply the principle of conservation of momentum. The momentum of an object is defined as the product of its mass and velocity.
The initial momentum of the bullet can be calculated by multiplying its mass by its initial velocity:
Initial momentum of bullet = mass of bullet × initial velocity of bullet
= 35 kg × 475 m/s
Since the block was at rest, its initial momentum is zero.
According to the law of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision.
So, the total momentum before the collision is:
Total initial momentum = Initial momentum of bullet + Initial momentum of block
= (35 kg × 475 m/s) + (2.5 kg × 0 m/s)
The total momentum after the collision is:
Total final momentum = Final momentum of bullet + Final momentum of block
= (35 kg × 275 m/s) + (2.5 kg × final velocity of block)
Since the bullet passes through the block and continues with a velocity of 275 m/s, the final momentum of the bullet is (mass of the bullet × final velocity of the bullet):
Final momentum of bullet = 35 kg × 275 m/s
Now, equating the total initial momentum to the total final momentum:
(35 kg × 475 m/s) + (2.5 kg × 0 m/s) = (35 kg × 275 m/s) + (2.5 kg × final velocity of block)
You can now solve this equation to find the final velocity of the block. Rearranging the equation, we get:
2.5 kg × final velocity of block = (35 kg × 475 m/s) - (35 kg × 275 m/s)
Finally, divide both sides by 2.5 kg to solve for the final velocity of the block:
Final velocity of block = [(35 kg × 475 m/s) - (35 kg × 275 m/s)] / 2.5 kg
Calculating the expression will give you the final velocity of the block after the bullet passes through it.