Aprojectile is launched from ground level with an initial speed of 53.7 m/s. find the launch angle (the angle the initial velocity vector is above the horizontal) such that the maximum height of the projectile is equal to its horizontal range. (ignore any effects due to air resistance.)

Awater slide of length l has a vertical drop of h. abby's mass is m. an average friction force of magnitude f opposes her motion. she starts down the slide at initial speed vi. use work-energy ideas to develop an expression for her speed at the bottom of the slide. then evaluate your result using unit analysis and limiting case analysis. express your answer in terms of the variables h, m, l, vi, f and appropriate constants. vf v f

How to tell if two objects are in thermal equilibrium 1.the objects have the same temperature 2.the objects are the same size 3.the objects are touching each other 4.the objects temperatures are changing

When the displacement of a mass on a spring is 12a the half of the amplitude, what fraction of the mechanical energy is kinetic energy? at what displacement, as a fraction of a, is the mechanical energy half kinetic and half potential?