What is the Mass of Your Faster Running Friend?

[a18c18]

Homework Statement

You run a race with your friend. At first you each have the same kinetic energy, but then you find that she is beating you. When you increase your speed by 21%, you are running at the same speed she is. If your mass is 77 kg, what is her mass?

Homework Equations

K=1/2mv^2

The Attempt at a Solution

K(initial me)=1/2*77*.79v
K(initial friend)=1/2*mass*v

1/2*77*.79v=1/2*mass*v

the v's cancel out so the mass should be 30.415/.5 or 60.83 but this is not the right answer. Does anyone know what I did wrong?

 

[Stovebolt]

You started out with the right idea for setting up the problem, but there are a few errors.

1. Check the math for the relative velocities. If you started out 21% slower than your friend, you were not going 0.79V_friend.

Try using V_friend = 1.21V_me.

2. Check the formula you used in your step 3. Velocity should be squared. Remember to calculate the entire term (1.21V)².

Once you make these changes, you should get the correct answer.

 

[a18c18]

Okay i got it. Thank you so much!