Question

Two objects of masses 2kg and 3kg are moving along the same straight line in the opposite direction with velocities of 4m/s and 2m/s respectively. They collide and after collision the first object moves at a velocity of 10m/s. Determine the velocity of the second object.

Answer 1

QUESTION:-

Two objects of masses 2kg and 3kg are moving along the same straight line in the opposite direction with velocities of 4m/s and 2m/s respectively. They collide and after collision the first object moves at a velocity of 10m/s. Determine the velocity of the second object.

EXPLANATION:-

Let the 1st object be A

And the 2nd object be B

Now,

Mass of A (m₁)=2 kg

Mass of B (m₂)=3 kg

Initial velocity of A(u₁)=4 m/s

Initial velocity of B(u₂)=2 m/s

Final velocity of A(v₁)=10 m/s

Final velocity of B(u₂)= TO BE CALCULATED

Let's calculate the initial momentum .

Initial momentum=m₁u₁+m₂u₂

Initial momentum=(2×4)+(3×2)

Initial momentum=8+6

Initial momentum=14 kg m/s

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Final momentum=m₁v₁+m₂v₂

Final momentum=(2×10)+(3×v₂)

Final momentum=20+3v₂

Acc to conservation of momentum-:

Final momentum=Initial momentum

20+3v₂=14

3v₂=14-20

3v₂=-6

v₂=-2 m/s

So the velocity of another object will be -2 m/s

[- sign depicts that the motion is in opposite direction]

Answer 2

Answer:

Two objects of masses 2kg and 3kg are moving along the same straight line in the opposite direction with velocities of 4m/s and 2m/s respectively. They collide and after the collision, the first object moves at a velocity of 10m/s, the velocity of the second object is $-6m/s$

Explanation:

• Momentum is conserved in every collision, that is after and before momentum should be the same

• When an object with masses $m_{1}$ with velocity $u_{1}$ and another object with mass $m_{2}$ and velocity $u_{2}$ collide with each other, after the collision the first object moves with velocity $v_{1}$ and the second one moves with velocity $v_{2}$,

• momentum before the collision is

        $m_{1} u_{1} +m_{2} u_{2}$

• momentum after collision is

        $m_{1} v_{1} +m_{2} v_{2}$

• then according to the momentum conservation

        $m_{1} u_{1} +m_{2} u_{2}=m_{1} v_{1} +m_{2} v_{2}$

From the question, we have

$m_{1} =2kg$

$m_{2} =3kg$

$u_{1} =4m/s$

$u_{2} =-2m/s$(opposite direction)

$v_{1} =10m/s$

put the values to get the velocity of the second object after the collision

$2*4+3*-2=2*10+3*v_{1}$

⇒

$-18=3v_{1} \\v_{1}=-18/3=-6m/s$