In relativity theory, velocities can be represented by points in a certain "rapidity space" in which the distance between two neighboring points is ds = [2/(1 r2)]./dr2 r 2 d02, where r and 0 are polar coordinates, and we consider just a two-dimensional space. (An expression like this for the distance in a non-Euclidean space is often called the metric of the space). Use the EulerLagrange equation to show that the shortest distance from the origin to any other point is a straight line.

Afisherman notices that his boat is moving up and down periodically without any horizontal motion, owing to waves on the surface of the water. it takes a time of 2.20 s for the boat to travel from its highest point to its lowest, a total distance of 0.670 m . the fisherman sees that the wave crests are spaced a horizontal distance of 5.80 m apart. (a) how much is the wavelength? (b) find the period of the wave. (c) how fast are the waves traveling? (d) what is the amplitude a of each wave?

If the textbook weighs 19.6 newtons on venus,what is the strength of gravity on venus?

Consider a system with two masses that are moving away from each other. why will the kinetic energy differ if the frame of reference is a stationary observer or one of the masses?