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.
What is their Kinetic Energy each?
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.
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.