A boy on a skateboard coasts along at 5 m / s . He has a...

A boy on a skateboard coasts along at $5 \mathrm{m} / \mathrm{s} .$ He has a ball that he can throw at a speed of $10 \mathrm{m} / \mathrm{s}$. What is the ball's speed relative to the ground if he throws the ball (a) forward or (b) backward?

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Key Concepts

Vector Addition

Vector addition is the mathematical operation used to combine two or more vectors, taking into account both their magnitudes and directions. In kinematics, especially when dealing with relative motion, vector addition allows for the calculation of an object's overall velocity when it is moving in a particular direction relative to another moving object.

Relative Velocity

Relative velocity is a measure of the velocity of one object as observed from another moving object. It is determined by appropriately adding or subtracting the velocities of the objects depending on their direction relative to each other, and is fundamental in understanding motion from different perspectives.

Frames of Reference

A frame of reference is the vantage point or coordinate system from which the position and motion of objects are measured. Changing the frame—such as switching between a moving observer and a stationary one—can result in different measured speeds, highlighting that velocity can be relative.

Sign Conventions

Sign conventions involve defining a positive and a negative direction in a coordinate system to ensure consistency in calculations. This concept is essential in relative motion problems to correctly add or subtract velocities based on the direction of movement.

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