Two football players are squared off against each other on the gridiron. Big Bubba has a mass of 125 kgs
but he's slower than a snail, only able to run at a measly 7 m/s. Lil' Pete, on the other side of the line, is a
skinny 80 kg, but can run like a rocket at -10 m/s. Assume that these two players are running directly at
each other and then, Wham!, they collide and bounce off of each other. To nobody's surprise, Lil' Pete
gets knocked backward with a velocity of +10 m/s; however, Big Bubba is also knocked backward: what is
Big Bubba's velocity after the collision?

-5.8 m/s

Explanation:

Given:-

- The mass of Big Bubba, mb = 125 kg

- The mass of Lil' Pete, mp = 80 kg

- The initial velocity of Big Bubba, vb = 7 m/s

- The initial velocity of Lil Pete , vp = -10 m/s

- The velocity after impact of Lil' Pete, vp' = + 10 m/s

- The velocity after impact of Big Bubba = vb'

Find:-

what is  Big Bubba's velocity after the collision?

Solution:-

- We will consider the two football players as particles of mass mb and mp with their respective velocities vb and vp heading towards each other.

- The masses collide and both reverse in direction with velocities vb' and vp'.

- The system of the two masses have no external forces acting on it; hence, the system is isolated from any fictitious forces.

- For above conditions we can apply the principle of conservation of linear momentum. The linear momentum of two football players before ( Pi ) and after the impact ( Pf ) remain constant. The conservation is:

                             Pi = Pf

           mb*vb + mp*vp = mb*vb' + mp*vp'

           mb*vb + mp*( vp - vp' ) = mb*vb'

- Develop an expression for Big Bubba's velocity after impact vb':

           vb' = vb + mp/mb*( vp - vp' )

- Plug in the values and evaluate:

         vb' = 7 + 80/125*( -10 - 10 )

         vb' = 7 - 80*20 / 125

          vb' = -5.8 m/s  

The velocity of Big Bubba after impact is vb' = -5.8 m/s

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