Question

Two objects of masses 300g and 400g are moving along the same line and direction with velocities of 3 m/s and 4 m/s, respectively? They collide and after the collision, the first object moves at a velocityof 1.48 m/s. Determine the velocity of second object.​

Answer 1

Answer:

Before Collision After collision

A B A B

100 g 200g → 100g 200g

2m/s 1m/s v=? 1.67ms

−1

Let the 100 g and 200 g objects be A and B as shown in above figure.

Initial momentum of A=

1000

100

×2=0.2kgms

−1

Initial momentum of B=

1000

200

×1=0.2kgms

−1

∴ Total momentum of A and B before collision

=0.2+0.2=0.4kgms

−1

Let the velocity of A after collision =v

∴ Momentum of A after collision =

1000

100

×v=0.1v

Also, momentum of B after collision

=

1000

200

×1.67=0.334kgms

−1

∴ Total momentum of A and B after collision

=0.1×v+0.334

Using the law of conservation of momentum, momentum of A and B after collision = momentum of A and B before collision

0.1×v+0.334=0.4

0.1×v=0.4−0.334

⇒v=

0.1

0.066

=0.66ms

−1

Answer 2

Explanation:

Before Collision                   After collision

A                    B                   A                  B

100 g           200g    →    100g          200g

2m/s             1m/s               v=?           1.67ms−1

Let the 100 g and 200 g objects be A and B as shown in above figure.

Initial momentum of A=1000100×2=0.2kgms−1

Initial momentum of B=1000200×1=0.2kgms−1

∴ Total momentum of A and B before collision

=0.2+0.2=0.4kgms−1

Let the velocity of A after collision =v

∴ Momentum of A after collision =1000100×v=0.1v

Also, momentum of B after collision

=1000200×1.67=0.334kgms−1

∴ Total momentum of A and B after collision

=0.1×v+0.334

Using the law of conservation of momentum, momentum of A and B after collision = momentum of A and B before collision

0.1×v+0.334=0.4

0.1×v=0.4−0.334

⇒v=0.10.066=0.66ms−1