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A particle is dropped from a finite heig...

A particle is dropped from a finite height `H` above the ground level under gravity . Due to air resistance acceleration of particle becomes `a=g-kv` in the direction of velocity. Where `k=` positive constant `&v=` speed of particle. Then which of the following graph`(s)` is `//` are possible `(t_(0)=` time when particle touches the ground `):`

A

B

C

D

Text Solution

Verified by Experts

The correct Answer is:
A, B, D
`(dv)/(dt)=g-kvunderset(0)overset(v)int(dv)/(g-kv)=underset(t=0)overset(t)int dt`
`-(1)/(-kv)ln((g-kv)/(g))=t`
`g-kv=ge^(-kt)v=(g)/(k)[1-e^(-kt)]`
`a=(g)/(k)[0-e^(-kt)(-k)]`
`=g e^(-kt)`
`V=(g)/(k)-(a)/(k)=-(a)/(k)+(a)/(k)`
`V-(g)/(k)=-(a)/(k)`
`kv-g=-a`
`a=g-kv`
`=-kv+g`
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