Betty Bodycheck (mB = 50.2 kg, vB = 22.0 km/h in the positive x-direction) and Sally Slasher (mS = 45.2 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 are their final kinetic energy?
Total or separately?
Write the two equations of conservation of momentum in x and y directions. Sinc e you know the final directions, you can solve for the two unkonwn speeds.
With the final speeds, you can compute the final kinetic energy of each person
I did that but i am not getting the right answer
ok does anyone know how to do this i need step by step help on this
To determine the final kinetic energy of Betty and Sally, we need to calculate the final velocities of each individual after the collision.
Let's break down the problem step by step:
Step 1: Convert the velocities to meters per second (m/s) for easier calculations.
- Betty's velocity, vB = 22.0 km/h in the positive x-direction, then vB = 22.0 km/h * (1000 m/km) / (60 min/h) / (60 s/min) = 6.11 m/s.
- Sally's velocity, vS = 28.0 km/h in the positive y-direction, then vS = 28.0 km/h * (1000 m/km) / (60 min/h) / (60 s/min) = 7.78 m/s.
Step 2: Analyze the collision. After the collision, Betty moves 76.0° counterclockwise from her original direction, while Sally moves 12.0° from the x-axis.
- Betty's final velocity consists of two components: one in the x-direction (vBx) and one in the y-direction (vBy).
- vBx = vB * cos(76.0°) is her velocity in the x-direction.
- vBy = vB * sin(76.0°) is her velocity in the y-direction.
- Sally's final velocity also has two components: one in the x-direction (vSx) and one in the y-direction (vSy).
- vSx = vS * cos(12.0°) is her velocity in the x-direction.
- vSy = vS * sin(12.0°) is her velocity in the y-direction.
Step 3: Calculate the final velocities.
- For Betty:
- vBx = 6.11 m/s * cos(76.0°) = -1.64 m/s (negative due to the counterclockwise rotation).
- vBy = 6.11 m/s * sin(76.0°) = 5.95 m/s (positive because she moved up in the y-direction).
- Betty's final velocity is (vBx, vBy) = (-1.64 m/s, 5.95 m/s).
- For Sally:
- vSx = 7.78 m/s * cos(12.0°) = 7.59 m/s (positive because she moved to the right in the x-direction).
- vSy = 7.78 m/s * sin(12.0°) = 1.62 m/s (positive because she moved up in the y-direction).
- Sally's final velocity is (vSx, vSy) = (7.59 m/s, 1.62 m/s).
Step 4: Calculate the final kinetic energy of each individual.
- The kinetic energy (KE) is given by KE = 0.5 * mass * velocity^2.
- For Betty:
- KE_Betty = 0.5 * mB * (vBx^2 + vBy^2) = 0.5 * 50.2 kg * ((-1.64 m/s)^2 + (5.95 m/s)^2) ≈ 854.0 J.
- For Sally:
- KE_Sally = 0.5 * mS * (vSx^2 + vSy^2) = 0.5 * 45.2 kg * ((7.59 m/s)^2 + (1.62 m/s)^2) ≈ 2088.9 J.
Therefore, Betty's final kinetic energy is approximately 854.0 J, and Sally's final kinetic energy is approximately 2088.9 J.