A father racing his son has 1/3 the kinetic energy of the son, who has 1/4 the mass of the father. The father speeds up by 1.8 m/s and then has the same kinetic energy as the son. What are the original speeds of (a) the father and (b) the son?

Answer 1

Son : m, v
Father : M, u
M=4m
mv²/2=3Mu²/2 =>
mv²/2=3•4mu²/2 =>
v²=12 u²…..(1)
mv²/2= M(u+1.8)²/2
mv²/2= 4m(u+1.8)²/2
v²= 4(u+1.8)² ….(2)
Substitute v² from (1) in (2)
12 u²=4(u+1.8)²
3u²=u²+3.6u+3.24
u²-1.8u-1.62 = 0
u=2.46 m/s
v=sqrt(12 u²) = 3.46u = 8.52 m/s