Question

NEED HELP ASAP

A 110kg 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. 

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Answer 1

Answers:

a) -2.54 m/s

b) -2351.25 J

Step-by-step explanation:

This problem can be solved by the Conservation of Momentum principle, which establishes that the initial momentum
`p_(o)` must be equal to the final momentum
`p_(f)`:

`p_(o)=p_(f)` (1)

Where:

`p_(o)=m_(1) V_(o) + m_(2) U_(o)` (2)

`p_(f)=(m_(1) + m_(2)) V_(f)` (3)

`m_(1)=110 kg` is the mass of the first football player

`V{o}=-7 m/s` is the velocity of the first football player (to the south)

`m_(2)=75 kg` is the mass of the second football player

`U_(o)=4 m/s` is the velocity of the second football player (to the north)

`V_(f)` 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):

`m_(1) V_(o) + m_(2) U_(o)=(m_(1) + m_(2)) V_(f)` (4)

Isolating
`V_(f)`:

`V_(f)=(m_(1) V_(o) + m_(2) U_(o))/(m_(1) + m_(2))` (5)

`V_(f)=((110 kg)(-7 m/s) + (75 kg) (4 m/s))/(110 kg + 75 kg)` (6)

`V_(f)=-2.54 m/s` (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
`\Delta K` is defined as:

`\Delta K=(1)/(2) m_(1)V_(f)^(2) - (1)/(2) m_(1)V_(o)^(2)` (8)

Simplifying:

`\Delta K=(1)/(2) m_(1)(V_(f)^(2) - V_(o)^(2))` (9)

`\Delta K=(1)/(2) 110 kg((-2.5 m/s)^(2) - (-7 m/s)^(2))` (10)

Finally:

`\Delta K=-2351.25 J` (10) Where the minus sign indicates the player's kinetic energy has decreased due to the perfectly inelastic collision