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During a football game, a receiver has just caught a pass and is standing still. Before he can move, a tackler, running at a velocity of 3.8 m/s, grabs and holds onto him so that they move off together with a velocity of 2.3 m/s. If the mass of the tackler is 130 kg, determine the mass of the receiver in kilograms. Assume momentum is conserved.

Respuesta :

Answer:

The mass of the receiver is 85 kg.

Explanation:

Given:

Mass of the tackler (M) = 130 kg

Mass of the receiver = 'm' (Assume)

Initial velocity of the receiver (u) = 0 m/s

Initial velocity of the tackler (U) = 3.8 m/s

Final combined velocity (v) = 2.3 m/s

So, as per question, the momentum is conserved. Therefore, the total initial momentum is equal to the total final momentum.

Total initial momentum is given as:

[tex]P_i=mu+MU\\\\P_i=0+130\times 3.8\\\\P_i=494\ kg\cdot m/s[/tex]

Total final momentum is given as:

[tex]P_f=(m+M)v\\\\P_f=(m+130)2.3[/tex]

Now, as per momentum conservation:

[tex]P_f=P_i\\\\(m+130)2.3=494\\\\m+130=\frac{494}{2.3}\\\\m=214.78-130\\\\m=84.78\ kg\approx85\ kg[/tex]

Therefore, the mass of the receiver is 85 kg.

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