A body of mass 20kg moving with a velocity of 80ms\(^{-1}\) collides with another body of mass 30kg moving with a velocity of 50ms\(^{-1}\). If they both mo...
Question 1 Report
A body of mass 20kg moving with a velocity of 80ms\(^{-1}\) collides with another body of mass 30kg moving with a velocity of 50ms\(^{-1}\). If they both moved in the same direction after collision, find their common velocity if they moved in the :
(a) same direction before collision ; (b) opposite direction before collision.
Answer Details
By conservation of linear momentum, total momentum before = total momentum after. After collision they move together with common velocity \(v\); total mass \(=20+30=50\,\text{kg}\).
(a) Same direction before collision. Take both velocities as positive:
\[20(80)+30(50)=50v\]
\[1600+1500=50v\Rightarrow3100=50v\Rightarrow v=62\ \text{m/s}\]
(b) Opposite directions before collision. Take the second body's velocity as negative:
\[20(80)+30(-50)=50v\]
\[1600-1500=50v\Rightarrow100=50v\Rightarrow v=2\ \text{m/s}\]
The positive result shows the combined body moves in the direction of the \(20\,\text{kg}\) body.
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