Asample of a radioactive isotope of an element contains 60 million atoms and is found to have a decay rate of 8 hundred atoms per year. what is the half-life of the isotope? (give your answer correct to at least two decimal places.)

Abatter hits the baseball a with an initial velocity of v0 = 110 ft/sec directly toward fielder b at an angle of 23° to the horizontal; the initial position of the ball is 2.2 ft above ground level. fielder b requires 0.44 sec to judge where the ball should be caught and begins moving to that position with constant speed. because of great experience, fielder b chooses his running speed so that he arrives at the “catch position” simultaneously with the baseball. the catch position is the field location at which the ball altitude is 8.4 ft. determine the velocity of the ball relative to the fielder at the instant the catch is made.

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?

Aprojectile is launched from ground level with an initial velocity of v 0 feet per second. neglecting air resistance, its height in feet t seconds after launch is given by s equals negative 16 t squared plus v 0 t. find the time(s) that the projectile will (a) reach a height of 192 ft and (b) return to the ground when v 0equals112 feet per second. (a) find the time(s) that the projectile will reach a height of 192 ft when v 0equals112 feet per second. select the correct choice below and, if necessary, fill in the answer box to complete your choice.