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Question

A heavy car A of mass 2000kg travelling at 10m/s has a head-on collision with a sports carB of mass 500kg. If both cars stop dead on colliding, what was the velocity of car B?


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Solution

Step 1. Given data

Mass of Car A, =2000kg

Speed of Car A, =10m/s

Mass of Car B, =500kg

We need to find speed of Car B, vB

Step 2. Formula used

The linear momentum P of an object is given by

P=mv

where m is the mass of the object and vthe velocity of the object

Step 3. Find the velocity of the car B

mA=2000kgmB=500kgvA=10m/s

We have to find the velocity of the car B before the collision.

After the collision, both cars stop. So after the collision, the velocity of the cars is zero.

According to the law of conservation of linear momentum, the sum of linear momentum of the car A and B before the collision is equal to the sum of linear momentum of the car A and Bafter the collision.

mAvA+mBvB=0vB=-mAvAmBvB=-2000×10500vB=-40m/s

Hence, the velocity of the car B is 40m/s.


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