A text book of elementary mechanics, for the use of colleges and schools . rate of 80 yardsper minute: What would be the direction and rate of motion ifthere were no current ? 32 KINEMATICS. [39. 7. A balloon has a velocity of 20 feet per second in an upwarddirection which makes an angle a with a vertical line: If its ve-locity vertically upward would be 1000 feet per minute, what isits horizontal velocity due to the wind ? What is a ? Composition and Resolution of Accelerations. 39. Composition and Resolution of Accelerations. The composition and resolution of velocities may be extendedalso t
A text book of elementary mechanics, for the use of colleges and schools . rate of 80 yardsper minute: What would be the direction and rate of motion ifthere were no current ? 32 KINEMATICS. [39. 7. A balloon has a velocity of 20 feet per second in an upwarddirection which makes an angle a with a vertical line: If its ve-locity vertically upward would be 1000 feet per minute, what isits horizontal velocity due to the wind ? What is a ? Composition and Resolution of Accelerations. 39. Composition and Resolution of Accelerations. The composition and resolution of velocities may be extendedalso to the case of uniform accelerations, the methodbeing in all -respects similar to that in the precedingarticles. The sides of the parallelogram here representthe component accelerations, and the diagonal the re-sultant acceleration. The simplest application of the principle of the reso-lution of Accelerations is to the case of motion down aninclined plane (40). 40. Motion down an Inclined Plane. The direction ofthe acceleration of gravity is that of a vertical line, and. Fig. 18. a body falls in this direction if entirely free: but a bodyon an inclined plane is only free to slide along it, and theacceleration is here that component of the whole accele-ration which is parallel to the plane: viz., g sin a. Let (Fig. IS) ac be taken to represent the verticalacceleration g: the directions of its components arerespectively parallel and perpendicular to the plane, and 40.] COMPOSITION OF MOTIONS. 33 are represented by ab and ad. But iac = If L/C = or,and therefore flki = he — ac sin a. That is, arf, or theacceleration down the plane, is equal to g sin a. The formulas of Art. 27, for a falling body, are thenapplicable to the case of a body sliding down a smoothinclined plane, if for g we write g sin a. That is : v = g sin a. t,s = \g sin a . f,v2 = 2g sin a. s. In the last formula, if the body descends from II to I,s = HL, and s sin a = IIK or h, the height of theplane; .-. v* = 2gh.
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