Two brothers are jogging, Josh and Drake. Josh has 1/2 the KE of Drake. Also, he is twice the mass of Drake. Plus, Josh had to increase his speed by 1.35 meters/second to achieve the same kinetic energy of Drake. What is the initial velocity?

Answer 1

JoshKE=1/2DrakeKE
1/2Mj vj^2=1/4 Md Vd^2
1/2 2Md Vj^2=1/4 Md Vd^2

Vj^2=1/4 Vd^2

Vj= 1/2 Vd

but Vj+1.35 yields..
1/2 *2Md(Vj+1.35)^2=1/2 Md Vd^2
2(Vj+1.35)^2=Vd^2
finally

2(Vj+1.35)^2=4Vj^2
Vj+1.35=Vj sqrt2
Vj=1.35/.414=
check all that.