Asian Physics Olympiad · Year 2017

Problems

Problem 1A small object is launched horizontally from the edge of a cliff of height $H$ above level ground with initial speed $v_0$ . Set the origin at launch, $x$ horizontal along the launch direction and $y$ upward; neglect air resistance and use $g=9.8\,\mathrm{m/s^2}$ . The ground is level and wide enough to catch it. (a) Find flight time and range $R$ . (b) Find the velocity components and speed just before impact. (c) Determine the trajectory angle below the horizontal at impact.Solutions: 1
Problem 2An ideal emf source $\mathcal E$ in series with internal resistance $r$ supplies a resistive load $R$ ; all components and wires remain at fixed temperature and the circuit is in steady state. (a) Find the current, source terminal voltage, and load power. (b) Find the value of $R$ for maximum load power and that maximum. (c) At the maximum-power condition, compare power delivered by the source with power dissipated internally and state the load-power efficiency.Solutions: 1
Problem 3Monochromatic light of wavelength $\lambda$ is incident normally on a transmission grating of spacing $d=3\lambda$ with many narrow parallel slits per unit length. Neglect absorption and consider principal maxima; angle $\theta$ is measured from the straight-through direction. (a) State the maximum condition and find the first-order angle. (b) List all observable orders and the largest order. (c) For a screen a distance $L$ from the grating, find the transverse position $y_1$ of the first-order maximum using exact geometry.Solutions: 1