Betty Bodycheck (mB = 50 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.
This appears to be a momentum conservation problem, but you forgot to ask a question.
The question is what are their final kinetic energy?
need help with this question does anyone know the answer
To analyze this scenario, we can break it down into several steps:
Step 1: Find the momentum before the collision
The momentum of an object is given by the formula: momentum = mass × velocity.
For Betty:
mb = 50 kg (mass of Betty)
vb = 22.0 km/h = 22.0 × (1000/3600) m/s = 6.11 m/s (velocity of Betty)
momentumB = mb × vb = 50 kg × 6.11 m/s = 305.5 kg·m/s
For Sally:
ms = 45.2 kg (mass of Sally)
vs = 28.0 km/h = 28.0 × (1000/3600) m/s = 7.78 m/s (velocity of Sally)
momentumS = ms × vs = 45.2 kg × 7.78 m/s = 351.9 kg·m/s
Step 2: Convert Betty's and Sally's velocities into components
To calculate the components of Betty's velocity, use the given angle of 76.0° counterclockwise from her original direction.
The x-component (vBx) can be found using the formula: vBx = vB × cos(θ)
The y-component (vBy) can be found using the formula: vBy = vB × sin(θ)
vBx = 6.11 m/s × cos(76.0°) ≈ 1.26 m/s (rounded to two decimal places)
vBy = 6.11 m/s × sin(76.0°) ≈ 5.94 m/s (rounded to two decimal places)
To calculate the components of Sally's velocity, use the given angle of 12.0° from the x-axis.
The x-component (vSx) can be found using the formula: vSx = vS × cos(θ)
The y-component (vSy) can be found using the formula: vSy = vS × sin(θ)
vSx = 7.78 m/s × cos(12.0°) ≈ 7.60 m/s (rounded to two decimal places)
vSy = 7.78 m/s × sin(12.0°) ≈ 1.62 m/s (rounded to two decimal places)
Step 3: Calculate the momentum after the collision
Since momentum is a vector quantity, we need to consider both the x and y components separately.
The final x-component momentum (pF_x) can be found by adding the x-component momenta of Betty and Sally after the collision.
The final y-component momentum (pF_y) can be found by adding the y-component momenta of Betty and Sally after the collision.
pF_x = mB × vBx + mS × vSx = 50 kg × 1.26 m/s + 45.2 kg × 7.60 m/s ≈ 637.84 kg·m/s (rounded to two decimal places)
pF_y = mB × vBy + mS × vSy = 50 kg × 5.94 m/s + 45.2 kg × 1.62 m/s ≈ 448.18 kg·m/s (rounded to two decimal places)
Step 4: Find the magnitude and angle of Betty's momentum after the collision
To determine the magnitude (PF) and angle (θF) of Betty's momentum after the collision, we can use the formula to calculate the magnitude and the inverse tangent function to calculate the angle.
PF = √(pF_x^2 + pF_y^2) ≈ √(637.84^2 + 448.18^2) ≈ 772.38 kg·m/s (rounded to two decimal places)
θF = atan(pF_y / pF_x) ≈ atan(448.18 kg·m/s / 637.84 kg·m/s) ≈ 34.47° (rounded to two decimal places)
Therefore, Betty's momentum after the collision is approximately 772.38 kg·m/s in a direction that is approximately 34.47° counterclockwise from her original direction.