Betty Bodycheck (mB = 60.0 kg, vB = 22.0 km/h in the positive x-direction) and Sally Slasher (mS = 46.3 kg, vS = 28.0 km/h in the positive y-direction) are both racing to get to a hockey puck. Immediately after the collision, Betty is heading in a direction that is 76.0° counterclockwise from her original direction, and Sally is heading back and to her right in a direction that is 12.0° from the x-axis.

Lots of algebra here.

Write the momentum equations in x and y directions, momentum has to be conserved in each direction.

Once you find the velocity of the two girls, you can find the KE of each. Energy is probably not conserved.

I found the velocity of the two girls. I found that Betty's velocity is 5.14 m/s and Sally's is 6.35 m/s. I'm just having with converting these into Kinetic Energy.

I'm just having trouble with coverting these into Kinetic Energy.

KE of each= 1/2 massgirl*v^2

Ok Thanks a lot for your help

To find the kinetic energy of each person, we need to calculate their velocities and masses first, and then use the formula for kinetic energy.

Given information:
Betty Bodycheck:
- Mass (mB) = 60.0 kg
- Initial velocity (vB) = 22.0 km/h in the positive x-direction
- Final direction: 76.0° counterclockwise from her original direction

Sally Slasher:
- Mass (mS) = 46.3 kg
- Initial velocity (vS) = 28.0 km/h in the positive y-direction
- Final direction: 12.0° from the x-axis

To calculate the velocities in the x and y directions, we need to convert the initial velocities from km/h to m/s and then use trigonometry.

1. Convert the initial velocities to m/s:
vB = 22.0 km/h * (1000 m/1 km) * (1 h/3600 s) = 6.11 m/s
vS = 28.0 km/h * (1000 m/1 km) * (1 h/3600 s) = 7.78 m/s

2. Calculate the x and y components of their velocities using trigonometry:
vx_B = vB * cos(0°) = vB * cos(0 rad) = vB * 1 = 6.11 m/s * 1 = 6.11 m/s
vy_B = vB * sin(0°) = vB * sin(0 rad) = vB * 0 = 6.11 m/s * 0 = 0 m/s

vx_S = vS * cos(12°)
vy_S = vS * sin(12°)

3. Calculate the final velocities using the components in the x and y directions:
vfx_B = vf * cos(76°)
vfy_B = vf * sin(76°)

vfx_S = vf * cos(102°)
vfy_S = vf * sin(102°)

4. Calculate the kinetic energy using the formula: KE = 1/2 * m * v^2
KE_B = 1/2 * mB * (vfx_B^2 + vfy_B^2)
KE_S = 1/2 * mS * (vfx_S^2 + vfy_S^2)

Plug in the calculated values to get the final answers for their kinetic energy.