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Physics LibreTexts

6.3C: Body thrown vertically upwards with initial speed v₀

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If we measure y upwards from the ground, the equation of motion is

¨y=gγv=γ(ˆv+v).

The first time integral is

v=ˆv+(v0+ˆv)eγt

and this is shown in Figure VI.9.

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It reaches a maximum height after time T, when v=0(at which time the acceleration is just g):

t+1γln(1+v0ˆv).

The second time integral (obtained by writing v as dydt in Equation 6.3.25) and the space integral (obtained by writing ¨y as vdvdy in the equation of motion) require some patience, but the results are

y=(v0+ˆvγ(1eγtˆvt,

v=v0γyˆvln(ˆv+v0ˆv+v).

These are illustrated in Figures VI.10 and VI.11.

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This page titled 6.3C: Body thrown vertically upwards with initial speed v₀ is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Jeremy Tatum via source content that was edited to the style and standards of the LibreTexts platform.

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