Question

Tow objects, each of mass 1.5 kg, are moving in the same straight line but in opposite directions. The velocity of each object is 2.5 meter per second before the collision during which they stick together. What will be the velocity of the combined object after collision?

Answer 1

Answer:

Let, the mass of 1st object=m1=1.5kg

the mass of 2nd object=m2=1.5kg

And ,

1st object be moving from left to right direction

Therefore,

2nd object must be moving from right to left direction

So,Velocity of -

1st object=u1=2.5m/s

2nd object=u2=-2.5m/s(oppo. direction)

So, total initial momentum of both objects=m1u1+m2u2

=((1.5*2.5)+(1.5*(-2.5)))kgm/s

=0

Since,

Total initial momentum before collision=Total final momentum after collision

Therefore,

Total final momentum of both objects=0

or,

m1v1+m2v2=0

or,

1.5kg*v1+1.5kg*v2=0

or,

1.5(v1+v2)=0

or,

v1+v2=0/1.5kg

=0

Thus,

Combined velocity of both objects after collision is 0m/s

Answer 2

$\bf{\underline{\underline{SOLUTION:}}}$

Since two objects of equal masses are moving in opposite direction with equal velocity therefore, the velocity of the objects after collision during which they stick together will be zero.

$\bf{\underline{\underline{Step\: by\: step \:explanation:}}}$

$\bf{\underline {Given:}}$

Mass of first object, $m_1=1.5\:kg$

Initial velocity of one object, $u_1=2.5\:m\:s^{-1}$

Initial velocity of second object, $u_2 = - 2.5 \:m\:s^{-1}$

( since second object is moving in opposite direction)

$\bf{\underline {To\:find:}}$

Final velocity of both the objects which stick after collision, $v =\:?$

We know that,

$m_1u_1+m_2u_2=m_1v_1+m_2v_2$

Substituting the values, we get

$1.5 ×2.5+1.5×(-2.5)=1.5 × v + 1.5 × v$

$3.75-3.75 = v (1.5+1.5)$

$v = \dfrac{0}{3.00}= 0$

Therefore final velocity of both the objects after collision will become zero.