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Say a father who has a mass that is two times that of his son is racing against him, and his kinetic energy is half of his son. When the father increases his speed by one m/s, the kinetic energies are equal.
I do this:
M = mass of father
V = velocity of father
0.5MV^2 = 0.5(0.5mv^2)
2MV^2 = mv^2
(4m)V^2 = mv^2
4V^2 = v^2
2V = v
0.5M(V+1)^2 = 0.5m(2V)^2
(V+1)^2 = 4V^2
V^2 + 2V + 1 = 4V^2
-3V^2 +2V + 1 = 0
(3V +1) (-V + 1)
V = 1, -1/3
so V = 1 m/s
However, my book says the speeds are 2.4 m/s and 4/8 m/s for father and son, respectively. What am I doing wrong?
I do this:
M = mass of father
V = velocity of father
0.5MV^2 = 0.5(0.5mv^2)
2MV^2 = mv^2
(4m)V^2 = mv^2
4V^2 = v^2
2V = v
0.5M(V+1)^2 = 0.5m(2V)^2
(V+1)^2 = 4V^2
V^2 + 2V + 1 = 4V^2
-3V^2 +2V + 1 = 0
(3V +1) (-V + 1)
V = 1, -1/3
so V = 1 m/s
However, my book says the speeds are 2.4 m/s and 4/8 m/s for father and son, respectively. What am I doing wrong?