A95kg fullback (football player for those not into sports) moving south with a speed of 5.0 m/s has a perfectly inelastic collision with a 90.0 kg opponent running north at 3.0 m/s.
(a) calculate the velocity of the players just after the tackle.
(b) calculate the decrease in total kinetic energy as a result of the collision.

a.  ,

b.  

Explanation:

To calculate the values in the  question, a deep understanding of perfect inelastic collision is important.

When two bodies undergo inelastic collision, two important parameters must be well understood i.e

Momentum: the momentum is always conserved in perfectly inelastic collision. i.e the total momentum after collision is the sum of the individual momentum before collision

Kinetic energy: Kinetic energy is not conserved due to dissipative force.

a.To calculate the velocity, we first find the total momentum before collision

Momentum of player 1

Momentum of player 2

Hence the total momentum

Note, since the direction of movement before collision is due south and  due north respectively we have to represent the velocity using the rectangular coordinate

Hence  

solving for the resultant velocity, we have

To calculate the direction of movement, we have

b. to calculate the decrease in total kinetic energy, before collision, the total kinetic was

And the final kinetic energy after collision is

The decrease in Kinetic energy is

The negative sign indicate a decrease in Kinetic energy

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