To find the final speed after two objects collide when they have different speeds before the collision, you need to consider the conservation of momentum. The total momentum before the collision is equal to the total momentum after the collision.
The momentum of an object is given by the product of its mass and velocity. Let's assume we have two objects: object 1 with mass m1 and initial velocity v1, and object 2 with mass m2 and initial velocity v2.
The conservation of momentum can be expressed as:
m1 * v1 + m2 * v2 = m1 * v1' + m2 * v2'
Where v1' and v2' are the final velocities of object 1 and object 2, respectively, after the collision.
To find the final velocities, you need to consider the type of collision. There are two common types:
Elastic Collision: In an elastic collision, both momentum and kinetic energy are conserved. This means that the total kinetic energy before the collision is equal to the total kinetic energy after the collision. To solve for the final velocities, you would need additional information such as the coefficients of restitution or other properties of the objects involved.
Inelastic Collision: In an inelastic collision, the objects stick together or deform upon collision. Momentum is conserved, but kinetic energy may not be conserved. In this case, you can use the conservation of momentum equation to solve for the final velocities.
It's important to note that the solution will depend on the specific details of the collision, such as the masses and initial velocities of the objects, as well as any additional information about the collision.