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:
![P_i=mu+MU\\\\P_i=0+130\times 3.8\\\\P_i=494\ kg\cdot m/s](https://tex.z-dn.net/?f=P_i%3Dmu%2BMU%5C%5C%5C%5CP_i%3D0%2B130%5Ctimes%203.8%5C%5C%5C%5CP_i%3D494%5C%20kg%5Ccdot%20m%2Fs)
Total final momentum is given as:
![P_f=(m+M)v\\\\P_f=(m+130)2.3](https://tex.z-dn.net/?f=P_f%3D%28m%2BM%29v%5C%5C%5C%5CP_f%3D%28m%2B130%292.3)
Now, as per momentum conservation:
![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](https://tex.z-dn.net/?f=P_f%3DP_i%5C%5C%5C%5C%28m%2B130%292.3%3D494%5C%5C%5C%5Cm%2B130%3D%5Cfrac%7B494%7D%7B2.3%7D%5C%5C%5C%5Cm%3D214.78-130%5C%5C%5C%5Cm%3D84.78%5C%20kg%5Capprox85%5C%20kg)
Therefore, the mass of the receiver is 85 kg.