- #1

JJBladester

Gold Member

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## Homework Statement

A projectile enters a resisting medium at x=0 with an initial velocity v

_{0}=900ft/s and travels 4in before coming to rest. Assuming that the velocity of the projectile is defined by the relation v=v

_{0}-kx, where v is expressed in ft/s and x is in feet, determine (a) the initial acceleration of the projectile, (b) the time required for the projectile to penetrate 3.9in into the resisting medium.

Answers: (a) -2.43x10

^{6}ft/s

^{2}(b) 1.366x10

^{-3}s

## Homework Equations

x

_{i}=0ft

v

_{i}=900ft/s

x

_{f}=4in=.33333ft

v=v

_{i}-kx

v

_{f}=0ft/s (rest)

a(x)=d/dx[v(x)]

## The Attempt at a Solution

v=v

_{i}-kx

0=900-k*.33333 ----> k=2700s

^{-1}

a(x)=d/dx[v(x)]=d/dx[v

_{i}-kx]=-k=-2700

The answer of -2.43x10

^{6}ft/s

^{2}is obviously not -2700.