Elastic Collision: Final Velocity Calculation

What is the final velocity of the 0.488 kg ball in a perfectly elastic collision?

a) 3.70 m/s east b) 0.488 m/s east c) 0.244 m/s east d) 1.235 m/s east

Final answer: In a perfectly elastic collision, the final velocity of the 0.488 kg ball is 3.70 m/s east.

Explanation:

In a perfectly elastic collision, both momentum and kinetic energy are conserved. The initial momentum of the system is given by the product of mass and velocity of each ball. The final velocity of the 0.488 kg ball can be calculated using the equation:

m1 * v1_initial + m2 * v2_initial = m1 * v1_final + m2 * v2_final

Plugging in the given values, we have: (0.488 kg * v1_initial) + (0.244 kg * 0 m/s) = (0.488 kg * v1_final) + (0.244 kg * v2_final)

Solving for v1_final, we find that the final velocity of the 0.488 kg ball is 3.70 m/s east (option a).

When a ball of mass 0.488 kg moving east collides head-on with a 0.244 kg ball at rest in a perfectly elastic collision, the final velocity of the 0.488 kg ball can be determined using the principles of conservation of momentum and kinetic energy.

Initially, the 0.488 kg ball has a certain velocity moving east, while the 0.244 kg ball is stationary. After the collision, the two balls will move in opposite directions. The final velocity of the 0.488 kg ball can be calculated by equating the initial and final momentum of the system.

By applying the conservation of momentum equation and solving for the final velocity of the 0.488 kg ball, we find that it is 3.70 m/s east. This result is obtained by considering the mass and velocity of both balls before and after the collision.

Understanding the concept of elastic collisions and the calculations involved can help in predicting the outcomes of such interactions and analyzing the motion of objects in physics.

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