displacements_material for students

Classical Velocity Addition

For simplicity, we restrict our consideration of velocity addition to one-dimensional motion. Classically, velocities add like regular numbers in one-dimensional motion. Suppose, for example, a girl is riding in a sled at a speed 1.0 m/s relative to an observer. She throws a snowball first forward, then backward at a speed of 1.5 m/s relative to the sled. We denote direction with plus and minus signs in one dimension; in this example, forward is positive. Let be the velocity of the sled relative to the Earth, the velocity of the snowball relative to the Earth-bound observer, and the velocity of the snowball relative to the sled.

Classically, velocities add like ordinary numbers in one-dimensional motion. Here the girl throws a snowball forward and then backward from a sled. The velocity of the sled relative to the Earth is 1m/s. The velocity of the snowball relative to the truck is υ_r, while its velocity relative to the Earth is u. Classically, u= υ₊ υ_r

Classical Velocity Addition

Thus, when the girl throws the snowball forward, 2.5m/s. It makes good intuitive sense that the snowball will head towards the Earth-bound observer faster, because it is thrown forward from a moving vehicle. When the girl throws the snowball backward, -0.5m/s. The minus sign means the snowball moves away from the Earth-bound observer.