Answer:
(a) 5.85 m/s
(b) 59.33 degrees North East
Explanation:
From the law of conservation of linear momentum, the sum of initial momentum equals the sum of final momentum.
East Momentum
[tex]mv = (M +m)v_e[/tex] where v and m represent velocity and mass, [tex]v_e[/tex] is common velocity, M is mass of linebacker while m is mass of halfback
[tex](85)(7.2) = (85 + 120)(v_e)\\v_e=2.985365854 m/s\\v_e\approx 2.99 m/s[/tex]
North Momentum
[tex]Mv = (m +M)v_n[/tex] where v and m represent velocity and mass, [tex]v_n[/tex] is common velocity, M is mass of linebacker while m is mass of halfback
[tex](120)(8.6) = (85 + 120)(v_n)\\v_n=5.034146341m/s \\v_n\approx 5.03 m/s[/tex]
Resultant velocity, [tex]v_r=\sqrt {v_e^{2}+v_n^{2}}[/tex]
Resultant velocity=[tex]\sqrt {2.99^{2}+5.03^{2}}=5.852780422 m/s\approx 5.85 m/s[/tex]
Direction=[tex]\tan^{-1}(\frac {v_n}{v_e})=\tan^{-1}(\frac {5.03}{2.99})=59.33107335\approx 59.33^{\circ}[/tex] North of East
