3 A \(\boldsymbol { \rho }\) rticle \(P 6\) mass \(m\) g falls frm rest \(\mathbf { d } \quad \mathrm { rg }\) avty. The re is a resistiv fo ce 6 mag td \(m k v ^ { 2 } \mathrm {~N}\), wh re \(v \mathrm {~ms} ^ { - 1 }\) is th se e \(\boldsymbol { C }\) after it \(\mathbf { h }\) s fallera id stan e \(x \mathrm {~m}\) ad \(k\) is a \(\mathbf { p }\) itie co tan.

1. Bys b in ra ra p p iate d fferen ial eq tin ,s how th t $$v ^ { 2 } = \frac { g } { k } \left( 1 - \mathrm { e } ^ { - 2 k x } \right)$$ [] It is \(\mathbf { N }\) it \(\mathbf { h } \mathrm { t } k = 0.01\). The speed of \(P \mathrm { w } \mathbf { h } \mathrm { n } x \mathbf { b } \mathrm {~cm}\) es larg ap \(\mathbf { o } \mathrm { ch } \mathrm { s } V \mathrm {~ms} ^ { - 1 }\).
2. 1. Fid \(V\) correct to 2 decimal places.
   2. Hen e fidw far \(P \mathbf { b }\) s fallenw \(\mathbf { b }\) n ts sp ed \(\mathrm { s } \frac { 1 } { 2 } V \mathrm {~ms} ^ { - 1 }\).
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      Two in fo m smo h sp res \(A\) ad \(B \mathbf { 6 }\) eq \(l\) radili masses \(m\) ad \(2 m\) resp ctie ly. Sp re \(B\) is at rest \(\mathbf { n }\) a smo hb izn al sn face. Sp ere \(A\) is mi \(\mathbf { g } \mathbf { n }\) th sn face with sp ed \(u\) at an ag e \(\mathbf { b } \boldsymbol { B }\) to th lin 6 cen res \(6 A\) and \(B\) wh n it cb lid s with \(B\) (see \(\dot { \mathbf { d } }\) ag am). Th ce fficien