Mathematics 9709 · AS & A Level · Energy, work and power

Energy, work and power — practice question

Particle $P$ is launched from the upper end of a smooth ramp with speed $u\,\text{m s}^{-1}$ and moves along the steepest descent. The ramp is $6.4\,\text{m}$ long and makes an angle of $30^\circ$ to the horizontal. At the same moment that $P$ is launched, a second particle $Q$ is let go from rest at a point $3.2\,\text{m}$ vertically above the foot of the ramp (see diagram). If $P$ and $Q$ arrive at the bottom of the ramp at the same time,
(a(i))[4]

Determine the value of $u$.

(a(ii))[2]

Determine the speed at which $P$ reaches the bottom of the ramp.

Worked solution & mark scheme

This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: Acceleration of $P$ given as $a_p = g\sin30^\circ$

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