During a football game two players collide, the first player is a running back of 90.0 kg and is traveling at
+2.34 m/s; the second is a linebacker with a mass of 89.8 kg. Both are traveling at –2.23 m/s after the
tackle (tackle = stuck together). What was the initial velocity of the linebacker?
Givens:
mr = 90.0 kg;
vri = + 2.34 m/s;
vrf = –2.23 m/s
ml = 89.8 kg;
vli = ?;
vlf = –2.23 m/s
Plan:
ri + li = rf + lf
(mr)(vri) + (ml)(vli) = (mr)(vrf) + (ml)(vlf) = (mr)(vf) + (ml)(vf) = (mr + ml)(vf)
(mr)(vri) + (ml)(vli) = (mr + ml)(vf)
Calculations:
(mr + ml) = 179.8 kg
(90.0 kg)(+2.34 m/s) + (89.8 kg)(vli) = (179.8 kg)( –2.23 m/s)
m
m
– 2.23 s – 90.0 kg +2.34 s
v𝑙𝑖 =
89.8 kg
m
m
– 400.954 kg s – 210.6 kg s
v𝑙𝑖 =
89.8 kg
m
– 611.554 kg s
v𝑙𝑖 =
89.8 kg
m
v𝑙𝑖 = – 6.8101781737193794
s
m
v𝑙𝑖 = – 6.81
s
179.8 kg