In a penalty kick, a soccer player kicks the ball from ground level with an initial velocity of 25.0 m/s, 20.0° above the horizontal. Assume that air resistance is negligible. What is the maximum height, ymax, of the soccer ball?

When a book falls from a shelf to the ground without anyone pushing on it, no work is done on the book. true or false

Three different objects, all with different masses, are initially at rest at the bottom of a set of steps. each step is of uniform height . the mass of each object is a multiple of the base mass : object 1 has mass 4..00m , object 2 has mass 1..96m , and object 3 has mass . when the objects are at the bottom of the steps, define the total gravitational potential energy of the three-object system to be zero. if the objects are then relocated as shown, what is the new total potential energy of the system? each answer requires the numerical coefficient to an algebraic expression. each algebraic expression is given using some combination of the variables , , and , where is the acceleration due to gravity. enter only the numerical coefficient. (example: if the answer is 1..23mgd , just enter 1.23)

An object weighs 40n in air, weighs 20n when submerged in water and 30n when submerged in a liquid of unknown density. what is the density of the liquid?