A110kg football player moving south with a speed of 7.0m/s has a perfectly inelastic collision with a 75kg opponent running north at 4.0m/s.

a) calculate the velocity of the players just after the tackle.

b) calculate the decrease in kinetic energy of the 110kg player after the collision. 

Answers:

a) -2.54 m/s

b) -2351.25 J

Explanation:

This problem can be solved by the Conservation of Momentum principle, which establishes that the initial momentum must be equal to the final momentum :  

(1)  

Where:  

(2)  

(3)

is the mass of the first football player

is the velocity of the first football player (to the south)

 is the mass of the second football player

is the velocity of the second football player (to the north)

is the final velocity of both football players

With this in mind, let's begin with the answers:

a) Velocity of the players just after the tackle

Substituting (2) and (3) in (1):

(4)  

Isolating :

(5)

(6)

(7) The negative sign indicates the direction of the final velocity, to the south

b) Decrease in kinetic energy of the 110kg player

The change in Kinetic energy is defined as:

(8)

Simplifying:

(9)

(10)

Finally:

(10) Where the minus sign indicates the player's kinetic energy has decreased due to the perfectly inelastic collision

answer: its c lololo