A student with a mass of 40.0 kg can throw a 5.00 -kg ball with a relative speed of 10.0 m / s

step 1 we have mass of the sun ms equals to 40 kg and mass of the ball m b that is equals to 5 kg and r

A student with a mass of 40.0 kg can throw a 5.00 -kg ball...

A student with a mass of $40.0 \mathrm{~kg}$ can throw a 5.00 -kg ball with a relative speed of $10.0 \mathrm{~m} / \mathrm{s}$. The student is standing at rest on a cart of mass $10.0 \mathrm{~kg}$ that can move without friction. If the student throws the ball horizontally, what will the velocity of the ball with respect to the ground be?

Key Concepts

Inertial Reference Frames

An inertial reference frame is one in which objects obey Newton’s laws of motion without the need to account for fictitious forces. In dynamics problems, analyzing motion from the ground frame (an inertial frame) and considering the velocities relative to that frame ensures that the conservation laws like momentum conservation are applied correctly. This is essential for accurately describing the resultant velocities after interactions like a person throwing a ball.

Conservation of Momentum

This principle states that in the absence of external forces, the total momentum of a system remains constant. In problems involving two or more interacting bodies, such as a person throwing an object, the momentum lost by one part of the system is exactly gained by the other. This concept is crucial for understanding how the motion of each part of the system changes when one component is accelerated in one direction.

Relative Velocity

Relative velocity refers to the speed of one object as observed from another moving object. In situations where an object is thrown or launched from a moving platform, the velocity of the thrown object with respect to the ground must be determined by combining its velocity relative to the moving system and the velocity of that system. This concept is important in correctly translating motion between different frames of reference.

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