184 Circular Motion and Other Applications of Newton’s LawsP6.66Let the x–axis point eastward, the y-axis upward, and the z-axis point southward.(a)The range is Zvgii=22sinθThe initial speed of the ball is thereforevgZii==°=sin.sin..29 8028596 053 0θafafm sThe time the ball is in the air is found from ∆yv ta tiyy=+122as053 048 04 902=°−.sin..m sm s2bgafejttgiving t=8 04.s .(b)vRixei==×°=286 40026 371035 086 4003796πφπcos.cos.smsm sej(c)360° of latitude corresponds to a distance of 2πRe, so 285 m is a change in latitude of∆φππ=FHGIKJ° =×FHGGIKJJ° =×−SRe23602856 37103602 561063afejafm2mdegrees..The final latitude is then φφφfi=−=°−°=°∆35 00 002 5634 997 4....The cup is moving eastward at a speed vRfxef=286 400πφcos
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