If the pressure of an encloed gas doubles when the volume of its container is reduced to half its size, the relationship of pressure and volume must be .

Aproton is projected into a uniform electric field that points vertically upward and has magnitude e. the initial velocity of the proton has a magnitude v0 and is directed at an angle a below the horizontal. (a) find the maximum distance hmax that the proton descends vertically below its initial elevation. you can ignore gravitational forces. (b) after what horizontal distance d does the proton return to its original elevation? (c) sketch the trajectory of the proton. (d) find the numerical values of hmax and dife = 500 n> c,v0 = 4.00 * 105 m> s,anda = 30.0°.