A paladin howitzer fires a 46.00 kg projectile towards a 1000 kg metal block resting on a frictionless surface. Just before impact, the projectile is traveling with a horizontal velocity of 529 m/s. After the collision, the embedded projectile and the metal block move along the frictionless surface continuing in the same direction. Calculate the final velocity of the projectile-metal block system. (Assume the projectile embeds in the metal block and does NOT explode, and neglect air resistance.)

~ I have tried this one like 5 times... i just don't get it, can someone explain it to me~

Conservation of momentum: Total momentum

before the collision = Total momentum
after the collision.

M1*V1+M2*V2 = M1*V+M2*V = (M1+M2)*V
46*529 + 1000*0 = 1046*V
Solve for V.

ur so dumb its so easy

To solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.

The momentum of an object is defined as the product of its mass and velocity. So, we can start by calculating the initial momentum of the projectile and the metal block.

Given:
Mass of the projectile (m1) = 46.00 kg
Velocity of the projectile before impact (v1) = 529 m/s
Mass of the metal block (m2) = 1000 kg

Initial momentum of the projectile (p1) = m1 * v1
Initial momentum of the metal block (p2) = m2 * 0 m/s (as the block is at rest initially)

Since the motion is happening in only the horizontal direction, the initial total momentum before the collision is given by:

Initial total momentum before collision = p1 + p2

Now, let's calculate the value:

Initial total momentum before collision = (m1 * v1) + (m2 * 0)

After the collision, the embedded projectile and the metal block move together as a system. Let's assume their final velocity as 'v_f'.

The final momentum of the system is given by the product of the total mass of the system (m1 + m2) and the final velocity (v_f).

The final total momentum of the system is given by:

Final total momentum after collision = (m1 + m2) * v_f

According to the principle of conservation of momentum, the initial total momentum before the collision is equal to the final total momentum after the collision. Therefore, we can set up the following equation:

(m1 * v1) + (m2 * 0) = (m1 + m2) * v_f

Now, we can use this equation to solve for the final velocity (v_f) of the projectile-metal block system.

To solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum before a collision is equal to the total momentum after the collision, assuming there are no external forces.

In this problem, we have a projectile and a metal block moving along a frictionless surface, so there are no external forces involved.

First, let's calculate the initial momentum of the system before the collision. The momentum of an object is given by the product of its mass and velocity. The mass of the projectile is 46.00 kg, and its initial horizontal velocity is given as 529 m/s. Therefore, the initial momentum of the projectile is:

Momentum of projectile = mass of projectile × initial velocity of projectile
= 46.00 kg × 529 m/s

Now, let's calculate the initial momentum of the metal block. Its mass is given as 1000 kg, and since it is at rest initially, its initial velocity is 0 m/s. Therefore, the initial momentum of the metal block is:

Momentum of metal block = mass of block × initial velocity of block
= 1000 kg × 0 m/s
= 0 kg⋅m/s

Since there are no other objects or forces involved in the system, the total initial momentum of the system is equal to the sum of the initial momentum of the projectile and the initial momentum of the metal block. So, we can write:

Total initial momentum = Momentum of projectile + Momentum of metal block

Since we've already calculated the values for the two momenta, let's substitute them into the equation:

Total initial momentum = (46.00 kg × 529 m/s) + (1000 kg × 0 m/s)

Next, we need to calculate the final momentum of the system after the collision. After the collision, the projectile and the metal block move together, so they have a common final velocity.

Let's call the final velocity of the projectile-metal block system as Vf. Therefore, the final momentum of the projectile-metal block system is:

Final momentum of system = Total mass of system × Final velocity of system
= (mass of projectile + mass of metal block) × Vf

Since we know the mass of the projectile (46.00 kg) and the mass of the metal block (1000 kg), we can substitute these values into the equation:

Final momentum of system = (46.00 kg + 1000 kg) × Vf

According to the principle of conservation of momentum, the total initial momentum is equal to the total final momentum. Therefore, we can set the two equations equal to each other to solve for the final velocity of the system:

Total initial momentum = Final momentum of system
(46.00 kg × 529 m/s) + (1000 kg × 0 m/s) = (46.00 kg + 1000 kg) × Vf

Now, we can solve for Vf.