The Elements of Statics And Dynamics

Cover The Elements of Statics And Dynamics
The Elements of Statics And Dynamics
S L Sidney Luxton Loney
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41. Time to a given height. The height h at which a body has arrived in time t is given by substituting g for/ in equation (2) of Art. 32, and is therefore given by h = ut- \gtf.
This is a quadratic equation with both roots positive ; the lesser root gives the time at which the body is at the given height on the way up, and the greater the time at which it is at the same height on the way down.
Thus the time that elapses before a body, which starts with a velocity of 64 feet per second, is at a
... height of 28 feet is given by 28 = 64<-16 2, whence t = \ or \.
Hence the particle is at the given height in half a second from the commencement of its motion, and again in 3 seconds afterwards.
42. Velocity at a given height.
The velocity v at a given height h is, by equation (3) of Art. 32, given by v 2 = u? - Igh.
Hence the velocity at a given height is independent of the time, and is therefore the same at the same point whether the body be going upwards or downwards.
43. Greatest height attained.


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