Respuesta :
The topic here is momentum.
When a collision is said to be elastic, it means that the colliding objects now travel at their own new, indivual and distinct velocities, often in different directions.
So we write that as,
(mass of football player x velocity of football player) + (mass of referee x velocity of referee) = (mass of football player x velocity of football player) + (mass of referee x velocity of referee)
(M × 8) + (80 × 0) = (M× 0) + (80 × 5)
8M = 400
M = 50 kg
With the application of formulas, the mass of football player will be 80kg
COLLISION
According to Newton's third law, in any action, there will be equal and opposite reaction.
Given that a football player runs at 8m/s and plows into a 80kg referee standing on the field causing the referee to fly forward at 5m/s. Let
- mass of the player [tex]M_{1}[/tex] = ?
- initial velocity of the player [tex]U_{1}[/tex] = 8m/s
- Final velocity of the player [tex]V_{1}[/tex]
- mass of the referee [tex]M_{2}[/tex] = 80 kg
- Initial velocity of the referee [tex]U_{2}[/tex] = 0 ( since he is at rest )
- Final velocity of the referee [tex]V_{2}[/tex] = 5 m/s
Since it is a perfectly elastic collision,
[tex]U_{1}[/tex] = [tex]V_{2}[/tex] - [tex]V_{1}[/tex] ........ (1)
[tex]M_{1}[/tex][tex]U_{1}[/tex] = [tex]M_{2}[/tex][tex]V_{2}[/tex] + [tex]M_{1}[/tex][tex]V_{1}[/tex] ........ (2)
Substitute all the necessary parameters into the equation (1)
8 = 5 - [tex]V_{1}[/tex]
[tex]V_{1}[/tex] = 8 - 5
[tex]V_{1}[/tex] = 3 m/s
Now, Substitute all the necessary parameters into the equation (2)
8[tex]M_{1}[/tex] = (80 x 5) + (3[tex]M_{1}[/tex])
8[tex]M_{1}[/tex] - 3[tex]M_{1}[/tex] = 400
5[tex]M_{1}[/tex] = 400
[tex]M_{1}[/tex] = 400/5
[tex]M_{1}[/tex] = 80kg
Therefore, the mass of football player will be 80kg
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