A 3.0-kilogram object initially at rest explodes and splits into three fragments. One fragment has a mass of 0.50 kg and flies off along the negative x axis at a speed of 2.8 m/s, and another has a mass of 1.3 kg and flies off along the negative y axis at a speed of 1.5 m/s. Required:
What are the speed and direction of the third fragment?

The speed and direction of the third fragment are 2 meters per second and 54.316º, respectively.

Explanation:

The object is not under the influence of any external force, meaning that Principle of Momentum Conservation to calculation of the velocity of the third fragment:

(1)

Where:

, , - Masses of the first, second and third fragments, in kilograms.

- Initial velocity of the object, in meters per second.

, , - Velocities of the first, second and third fragments, in meters per second.

If we know that , , , , and , the velocity of the third fragment is:

The speed of the third fragment is the magnitude of the result found above:

And the direction of the third fragment is:

The speed and direction of the third fragment are 2 meters per second and 54.316º, respectively.

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