(i)[3]
Show that, as $P$ moves up the plane, $\frac{dv}{dt} = -2.5(3 + v)$.
(ii)[4]
Calculate the value of $T$.
(iii)[5]
Calculate the speed of $P$ at $t = 2T$.
Mathematics 9709 · AS & A Level · Probability
Probability — practice question
Particle $P$, with mass $0.2\,\text{kg}$, is launched at speed $2\,\text{m s}^{-1}$ up a path of maximum gradient on a plane that is inclined at $30^\circ$ to the horizontal (see diagram). A resistive force from air of size $0.5v\,\text{N}$ acts against the motion of $P$, where $v\,\text{m s}^{-1}$ denotes the speed of $P$ at time $t$ s after projection. The coefficient of friction between $P$ and the plane is $\frac{1}{2\sqrt{3}}$. The particle $P$ comes to instantaneous rest when $t = T$.