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
What is their final Kinetic Energy?
ok so how do i find each girls velocity after the collision because i know how to find the kinetic engery
To find the final velocities of both Betty and Sally after the collision, we can use the principles of conservation of momentum and conservation of kinetic energy.
1. Convert the velocities of Betty and Sally from km/h to m/s:
- Betty's velocity (vB) = 22.0 km/h * (1000 m/1 km) * (1 h/3600 s) ≈ 6.11 m/s
- Sally's velocity (vS) = 28.0 km/h * (1000 m/1 km) * (1 h/3600 s) ≈ 7.78 m/s
2. Calculate the initial momenta for Betty and Sally before the collision:
- Initial momentum of Betty (pB) = mB * vB
- Initial momentum of Sally (pS) = mS * vS
3. Calculate the total initial momentum before the collision:
- Initial total momentum (pInitial) = pB + pS
4. Use trigonometry to break down the final velocity of Betty after the collision into its x-component (vBx) and y-component (vBy):
- vBx = vB * cos(76.0°)
- vBy = vB * sin(76.0°)
5. Use trigonometry to find the x-component and y-component of Sally's final velocity after the collision:
- vSx = vS * cos(12.0°)
- vSy = vS * sin(12.0°)
6. Calculate the final momentum for Betty and Sally after the collision:
- Final momentum of Betty (pBf) = mB * vBx
- Final momentum of Sally (pSf) = mS * vSx
7. Calculate the total final momentum after the collision:
- Final total momentum (pFinal) = pBf + pSf
8. Apply the principle of conservation of momentum to find the final velocities of Betty and Sally:
- pInitial = pFinal
- pB + pS = pBf + pSf
9. Finally, use the principles of conservation of kinetic energy to calculate the final velocities of Betty and Sally:
- (1/2) * mB * vB^2 + (1/2) * mS * vS^2 = (1/2) * mB * vBf^2 + (1/2) * mS * vSf^2
Solving these equations will give you the final velocities for Betty and Sally.