A 10.0kg cart traveling East at 5.00 m/s collides with a 7.50kg cart traveling 3.00m/s at an angle of 55.0o. The two carts collide and stick together. What is the velocity of the cars after they stick together?

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.

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Step-by-step explanation: