A particle is shot moving vertically down into a body ofwater. At the water surf

Question

A particle is shot moving vertically down into a body ofwater. At the water surface V = 60 m/s. Waterresistance decelerates the particle according to a =(-0.5v^3). I need to determine the particle's velocity andposition a few seconds after impact with the water. I amhaving problems working through the calc. for this one, fairlysolid on the concept, ~ 10yrs. since calc classes. Thanks inadvance. A particle is shot moving vertically down into a body ofwater. At the water surface V = 60 m/s. Waterresistance decelerates the particle according to a =(-0.5v^3). I need to determine the particle's velocity andposition a few seconds after impact with the water. I amhaving problems working through the calc. for this one, fairlysolid on the concept, ~ 10yrs. since calc classes. Thanks inadvance.

Explanation / Answer

a = dv/dt = -.5v3 => dv/v3 = -.5dt => -[v-2]60->v /2 = -.5 [t]0->t=> 1/v2 - 1/3600 = t

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