Aball is thrown with an initial speed vi at an angle i with the horizontal. the horizontal range of the ball is r, and the ball reaches a maximum height r/6. in terms of r and g, find (a) the time the ball is in motion, (b) the ball’s speed at the peak of its path, (c) the initial vertical component of its velocity, (d) its initial speed, and (e) the angle i . (f) suppose the ball is thrown at the same initial speed found in part (d) but at the angle appropriate for reaching the maximum height. find this height. (g) sup- pose the ball is thrown at the same initial speed but at the angle necessary for maximum range. find this range.

Aneutron and a proton combine to form a nucleus. why does the mass of the nucleus differ from the sum of the masses of the individual nucleons?

Air is held within a frictionless piston-cylinder container, which is oriented vertically. the mass of the piston is 0.45 kg and the cross-sectional area is 0.0030 m2. initially (state 1) the pressure of the gas is sufficient to support the weight of the piston as well as the force exerted by the atmospheric pressure ( 101.32 kpa). the volume occupied by the air within the cylinder in state 1 is 1.00 liter. one end of a spring (with spring constant k = 1000 n/m) is attached to the top of the piston, while the other end of the spring is attached to a stage that can move vertically. initially the spring is undeflected and therefore exerts no force. then the stage is then moved quasistatically downward a distance of 10.0 cm, at which point the system reaches state 2. the piston-cylinder is not insulated; rather it remains in diathermal contact with the surroundings, which are at a constant temperature of 300 k. what is the change of pressure within the container?

Argon, neon, and xenon are examples of