Question

4) If an object of 40 kg is moving east at 20 m/s and collides with a 20 kg object moving along the same vector at 10 m/s, what will be the velocity of the smaller object if the larger object slows to 10 m/s?

Answer 1

`v_2_2=30m/s`

Step-by-step explanation:

In all collisions the total linear momentum of the system is conserved. Therefore:

`p_i=p_f\\\\Where:\\\\p_i=m_1_1 v_1_1+m_2_1 v_2_1\\\\p_f=m_1_2 v_1_2+m_2_2 v_2_2`

So,
`p_i` represents the linear momentum before the collision and
`p_f` represents the linear momentum after the collision. Now, let:

`m_1_1=Mass\hspace{3} of\hspace{3} the\hspace{3} bigger\hspace{3} o bject\hspace{3}before\hspace{3}the\hspace{3}collision\\v_1_1=Velocity \hspace{3} of\hspace{3} the\hspace{3} bigger\hspace{3} o bject\hspace{3}before\hspace{3}the\hspace{3}collision\\m_2_1=Mass\hspace{3} of\hspace{3} the\hspace{3} smaller\hspace{3} o bject\hspace{3}before\hspace{3}the\hspace{3}collision\\v_2_1=Velocity \hspace{3} of\hspace{3} the\hspace{3} smaller\hspace{3} o bject\hspace{3}before\hspace{3}the\hspace{3}collision`

`m_1_2=Mass\hspace{3} of\hspace{3} the\hspace{3} bigger\hspace{3} o bject\hspace{3}after\hspace{3}the\hspace{3}collision\\v_1_2=Velocity \hspace{3} of\hspace{3} the\hspace{3} bigger\hspace{3} o bject\hspace{3}after\hspace{3}the\hspace{3}collision\\m_2_2=Mass\hspace{3} of\hspace{3} the\hspace{3} smaller\hspace{3} o bject\hspace{3}after\hspace{3}the\hspace{3}collision\\`

`v_2_2=Velocity \hspace{3} of\hspace{3} the\hspace{3} smaller\hspace{3} o bject\hspace{3}after\hspace{3}the\hspace{3}collision`

According to the data provided by the problem:

`m_1_1=40kg\\v_1_1=20m/s\\m_2_1=20kg\\v_2_2=10m/s\\m_1_2=40kg\\v_1_2=10m/s\\m_2_2=20kg\\v_2_2=$\text{?}`

Replacing the data into the linear momentum equation and solving for
`v_2_2`:

`m_1_1 v_1_1+m_2_1v_2_1=m_1_2 v_1_2+m_2_2 v_2_2\\\\(40)(20)+(20)(10)=(40)(10)+20(v_2_2)\\\\800+200=400+20(v_2_2)\\\\20(v_2_2)=600\\\\ (v_2_2)=(600)/(20) =30m/s`

Thus, the velocity of the smaller object after the collision is 30m/s

Answer 2

The smaller object will move at 30 m/s

Step-by-step explanation:

From the principle of conservation of linear momentum,

Momentum of objects before collision = momentum of objects after collision.

`m_(1)v_(1) + m_(2)v_(2)=m_(1)v_(3)+m_(2)v_(4)`

where
`m_(1), m_(2) , v_(1)and v_(2)` are the masses and velocities of the objects 1 and 2 respectively before collision.

`40* 20 + 20* 10 = 40* 10 + 20* v_(4)`

`1000= 400 + 20v_(4)`

`v_(4)=30m/s`

Hence, the object will move at 30 m/s