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?

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oeerivona oeerivona · Answer 1 · 2020-12-08T02:13:10+01:00

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.