A 4kg and 5kg bodies moving on a frictionless horizontal surface at a velocity of ( -6i )m/s and ( +3 )m/s respectively. Collide a head on elastic collision. What is the velocity ( magnitude and direction) of the each body after collision?

4 kg → +4 m/s

5 kg → -5 m/s

Explanation:

The law of conservation of momentum states that:

You'll notice that we have two missing variables: v₁' & v₂'. Assuming this is a perfectly elastic collision, we can use the conservation of kinetic energy to set the initial and final velocities of the individual bodies equal to each other.

Let's substitute all known variables into the first equation.

Let's substitute the known variables into the second equation.

Now we have a system of equations where we can solve for v₁ and v₂.

Use the elimination method and multiply the bottom equation by -4.

Add the equations together.

The final velocity of the second body (5 kg) is -5 m/s. Substitute this value into one of the equations in the system to find v₁.  

The final velocity of the first body (4 kg) is 4 m/s.

We can verify our answer by making sure that the law of conservation of momentum is followed.

The combined momentum of the bodies before the collision is equal to the combined momentum of the bodies after the collision. [✓]

answer: the correct answer is 1.

explanation: there are various process in which a radioactive nuclei decays:

1) alpha decay: in this process, a heavier nuclei decays into lighter nuclei by releasing alpha particle. the mass number is reduced by 4 units.

2) electron capture: in this decay process, a parent nuclei absorbs an electron and gets converted into a neutron. simply, a proton and an electron combines together to form a neutron. mass number does not change in this process.

3) gamma ray emission: it is a decay process in which an unstable nuclei gives excess energy by a spontaneous electromagnetic process. this decay releases . this process does not change the mass number.

4) positron emission: it is a type of decay process, in which a proton gets converted to neutron and an electron neutrino. this is also known as -decay. in this the mass number remains same.

from the above information, we see that only alpha-decay is producing a change in the mass number of the nucleus.

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