# Kinetic Energy of a jogger problem

destinc
Jogger A has a mass m and a speed v, jogger B has a mass m/2 and a speed 3v, jogger C has a mass 3m and a speed v/2 and jogger D has a mass 4m and a speed v/2. Rank the joggers in order of increasing kinetic energy. Indicate ties where appropriate

I started with KE formula, KE=1/2mv^2 and plugged in values for each jogger
Jogger A KE=1/2mv^2
Jogger B KE=1/2(m/2)(3v)^2 which = 2.25mv^2
Jogger C KE=1/2(3m)(v/2)^2 which =6mv^2
Jogger D KE=1/2(4m)(v/2)^2 which =8mv^2

Based on this I ranked them in increasing order A,B,C,D
The answer given is, D<A = D<B
I'm not sure I understand the answer, and I don't see where I went wrong.
Thank you for any help.

Mentor
Jogger A has a mass m and a speed v, jogger B has a mass m/2 and a speed 3v, jogger C has a mass 3m and a speed v/2 and jogger D has a mass 4m and a speed v/2. Rank the joggers in order of increasing kinetic energy. Indicate ties where appropriate

I started with KE formula, KE=1/2mv^2 and plugged in values for each jogger
Jogger A KE=1/2mv^2
Jogger B KE=1/2(m/2)(3v)^2 which = 2.25mv^2
Jogger C KE=1/2(3m)(v/2)^2 which =6mv^2
Jogger D KE=1/2(4m)(v/2)^2 which =8mv^2

Based on this I ranked them in increasing order A,B,C,D
The answer given is, D<A = D<B
I'm not sure I understand the answer, and I don't see where I went wrong.
Thank you for any help.

Check your math for joggers C and D.

Mentor
I started with KE formula, KE=1/2mv^2 and plugged in values for each jogger
Jogger A KE=1/2mv^2
Jogger B KE=1/2(m/2)(3v)^2 which = 2.25mv^2
Good.
Jogger C KE=1/2(3m)(v/2)^2 which =6mv^2
Jogger D KE=1/2(4m)(v/2)^2 which =8mv^2
Redo these.

destinc
Jogger C KE=1/2(3m(v/2)^2 = 3/2m(v^2)/4 = 3/8mv^2
Jogger D KE= 1/2(4m)(v/2)^2 = 1/2mv^2
Which means D=A and both > C > B
Which still isn't the given answer

Mentor
Jogger C KE=1/2(3m(v/2)^2 = 3/2m(v^2)/4 = 3/8mv^2
Jogger D KE= 1/2(4m)(v/2)^2 = 1/2mv^2
Which means D=A and both > C > B
Which still isn't the given answer

List all four results now that you've recalculated.

Mentor
Jogger C KE=1/2(3m(v/2)^2 = 3/2m(v^2)/4 = 3/8mv^2
Jogger D KE= 1/2(4m)(v/2)^2 = 1/2mv^2
Right.
Which means D=A
OK.
and both > C > B
Rethink that.

destinc
Jogger A KE= 1/2mv^2
Jogger B KE= 2.25mv^2
Jogger C KE= 3/8mv^2
Jogger D KE=1/2mv^2

Oh C< D=A < B Still not the answer
Thanks again for all this help

Mentor
The answer given is, D<A = D<B
Obviously a typo here. Better check it. (that first D should be a C)

destinc
I really don't understand the format of the given answer, could one of you translate, why don't they give value of C in the answer?

destinc
ahhhhh, Typo is in book. Thanks for the help