Paper 5 October/November 2009 MATHEMATICS (9709/51) A Levels
لطفا برای اطمینان از عملکرد و تجربه بهتر از مرورگرهای مدرن و به روز مانند کروم یا فایرفاکس استفاده کنید.

A ball of mass $0.05{\text{ }}kg$ is released from rest at a height $h{\text{ }}m$ above the ground. At time $t\,s$ after its release, the downward velocity of the ball is $vm{\text{ }}{s^{ - 1}}$. Air resistance opposes the motion of the ball with a force of magnitude $0.01v{\text{ }}N$.
a) Show that $\frac{{dv}}{{dt}} = 10 - 0.2v$. Hence find $v$ in terms of $t$.
b) Given that the ball reaches the ground when $t = 2$, calculate $h$.