Respuesta :
Answer:
The magnitude of the velocity of the cars after they stick is approximately 3.7 m/s
Step-by-step explanation:
The given parameters are;
The mass of the cart traveling East, m₁ = 10.0 kg
The speed of the cart traveling East v₁= 5.00 m/s
The mass of the cart traveling at an angle of 55° m₂= 7.50 kg
The speed of the cart traveling at an angle of 55°, v₂ = 3.00 m/s
The component of the velocities of the cart raveling at an angle are given as follows;
v = 3.00 × cos(55°)·i + 3.00 × sin(55°)·j
The total momentum before collision = m₁ × v₁ + m₂ × v₂ by substitution is therefore;
m₁ × v₁ + m₂ × v₂ = 10 × 5.00·i + 7.5 × (3.00 × cos(55°)·i + 3.00 × sin(55°)·j)
The total momentum after collision = (m₁ + m₂) × v₃
By the principle of the conservation of linear momentum, whereby the momentum is conserved, we have;
m₁ × v₁ + m₂ × v₂ = (m₁ + m₂) × v₃
10 × 5.00·i + 7.5 × (3.00 × cos(55°)·i + 3.00 × sin(55°)·j) = (10 + 7.5) × v₃
50.00·i + 12.91·i + 18.43·j = 17.5·v₃
62.91·i + 18.43·j = 17.5·v₃
∴ v₃ = (62.91·i + 18.43·j)/17.5 ≈ 3.59·i + 1.05·j
Therefore, the magnitude of the velocity of the cars after they stick = √(3.59² + 1.053²) ≈ 3.7
The magnitude of the velocity of the cars after they stick ≈ 3.7 m/s.
