Final Answer:
The final speed of the two objects after they collide and stick together is v/2.
Step-by-step explanation:
When two objects moving in opposite directions with speed v collide and stick together, the conservation of momentum can be used to find their final speed.
According to the law of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision. Mathematically, this can be expressed as m1v1 + m2v2 = (m1 + m2)v_final, where m1 and m2 are the masses of the two objects, v1 and v2 are their initial velocities, and v_final is their final velocity.
Since the two objects stick together after the collision, their combined mass is (m1 + m2). Therefore, using the given information that they move with a speed of v/2 after the collision, we can solve for v_final.
Substituting the given values into the equation, we have m1(-v) + m2v = (m1 + m2)(v/2). Simplifying this equation gives us -m1v + m2v = (m1 + m2)(v/2), which further simplifies to (m1 + m2)v/2 = (m1 + m2)(v/2). Canceling out (m1 + m2) from both sides gives us v_final = v/2.
Therefore, the final speed of the two objects after they collide and stick together is v/2.