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A drone car with a mass of 2000 kg is traveling down the road at 21 m/s. It collides with another drone car half of the mass moving at -15 m/s. After the collision, the 2000 kg car is moving at -3.1 m/s. What is the speed of the other drone car after the collision?

Respuesta :

MrRoyal

Answer:

[tex]v_2 = 33.2m/s[/tex]

Explanation:

Given

Before Collision

[tex]m_1 = 2000kg[/tex]

[tex]u_1 = 21m/s[/tex]

[tex]m_2 = 1000kg[/tex]

[tex]u_2 = -15m/s[/tex]

After Collision

[tex]m_1 = 2000kg[/tex]

[tex]v_1 = -3.1m/s[/tex]

[tex]m_2 = 1000kg[/tex]

[tex]v_2 = ???[/tex] ------ Required

As analyzed above;

To solve for v2, we simply make use of the law of conservation of momentum formula;

which states:

[tex]m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2[/tex]

Substitute values in the above formula

[tex]2000 * 21 + 1000 * -15 = 2000 * -3.1 + 1000 * v_2[/tex]

[tex]42000 - 15000 = -6200 + 1000v_2[/tex]

[tex]27000 = -6200 + 1000v_2[/tex]

Collect Like Terms

[tex]27000 + 6200 =1000v_2[/tex]

[tex]33200 =1000v_2[/tex]

Divide through by 1000

[tex]v_2 = \frac{33200}{1000}[/tex]

[tex]v_2 = 33.2m/s[/tex]

Hence, the speed the other drone is 33.2m/s