A 5 gram bullet is fired and embeds into a 30 gram block of wood resting on a 2 m tall post. After the collision, the piece of wood lands 15 meters from the base of the post. Find the initial speed of the bullet.
To find the initial speed of the bullet, we need to use the principle of conservation of momentum. The momentum before the collision is equal to the momentum after the collision.
Here are the steps to find the initial speed of the bullet:
1. Determine the momentum before the collision:
The momentum of an object is given by the product of its mass and velocity. Before the collision, the only object in motion is the bullet, so the momentum is calculated as:
Momentum_before = mass_bullet * velocity_bullet
2. Determine the momentum after the collision:
After the collision, the bullet embeds into the block of wood, so the momentum is transferred to the combined system of the bullet and the wood. The total momentum is given by the sum of the momentums of the bullet and the wood.
To calculate the momentum of the wood, we need to find its velocity. Since the wood lands after the collision, we can use the equation of motion:
s = ut + 0.5 * a * t^2
where s = 15 m (distance), u = initial velocity of the wood (unknown), a = acceleration (9.8 m/s^2 due to gravity), and t is the time taken for the wood to fall.
The time taken for the wood to fall can be calculated using the equation:
s = 0.5 * g * t^2
where g = 9.8 m/s^2 (acceleration due to gravity).
Solve this equation for t and substitute the value in the equation of motion to find the initial velocity of the wood (u).
Momentum_after = (mass_bullet + mass_wood) * velocity_wood
3. Apply the conservation of momentum principle:
According to the conservation of momentum principle:
Momentum_before = Momentum_after
Substitute the values from steps 1 and 2, and solve the equation for the initial velocity of the bullet (velocity_bullet).
Following these steps, we can find the initial speed of the bullet.