1. The diagram above illustrates the trajectory of a fired missile from point $P$ at $250 \, \text{ms}^{-1}$.
   If the missile reaches point $Q$ after $40 \, \text{s}$, calculate the distance $|PQ|$.

2. State three properties of a semiconductor.

3. The effective potential energy, $E$, of a lunar satellite of mass $m$, moving in an elliptical orbit around the moon of mass $M$, is given by:

where $r$ is the distance of the satellite from the moon and $G$ is the universal gravitational constant with dimensions $M^{-1} L^3 T^{-2}$.
Determine the dimensions of the angular momentum, $K$, of the satellite using dimensional analysis.

4. A $50 \, \text{N}$ force is applied to the free end of a spiral spring with a force constant of $100 \, \text{Nm}^{-1}$.
   Calculate the work done by the force to stretch the spring.

5. (a) What is a geostationary satellite?
   (b) Name two types of lasers.

6. State:
   (a) The S.I. unit of the intensity of blackbody radiation.
   (b) Two features of the intensity-wavelength graph of a perfect blackbody at different temperatures.

7. State three differences between magnetic and non-magnetic materials.

8. (a) (i) State the law of inertia.
   (ii) Use the law stated in (a)(i) to explain how wearing a safety belt in a moving vehicle reduces the possibility of severe injuries during a collision.

   (b) (i) Define the moment of a force.
   (ii) A uniform plank measures $2 \, \text{m}$ long from point $A$ to $B$. If the weight of the plank is $54 \, \text{N}$ and it rests on a knife-edge $0.50 \, \text{m}$ from end $B$, with point $A$ supported by a vertical string so that $AB$ balances horizontally:

   • Draw a force diagram for the arrangement.
   • Determine the tension, $T$, in the string.
   • Determine the force, $F$, acting on the knife edge.

   (c) State three differences between solid friction and viscosity.
   (d) State one method of increasing the velocity ratio of a pulley system.

9. (a) (i) State Coulomb's law of electrostatics.
   (ii) The electron and proton of a hydrogen atom are separated by a mean distance of $5.2 \times 10^{-11} \, \text{m}$. Calculate the magnitude of the electrostatic force between them.
   [$e = 1.6 \times 10^{-19} \, \text{C}$, $(4\pi \epsilon_0)^{-1} = 9.0 \times 10^9 \, \text{Nm}^2/\text{C}^2$]

   (b) The diagram above shows a potential divider circuit.

   • Show that $V_{\text{out}} = V_{\text{in}} \left(\frac{R_1}{R_1 + R_2}\right)$.
   • If $\frac{V_{\text{in}}}{V_{\text{out}}} = 2.5$ and $R_2 = 30 \, \Omega$, calculate $R_1$.
   • Define the volt.

   (c) Explain why wood is not suitable for use as the core of transformers.
   (d) State one application of the cathode ray tube.

10. (a) State one condition necessary for each of the following:
    (i) Constructive interference of waves.
    (ii) Total internal reflection.
    (iii) Production of beats.

    (b) In a resonance tube experiment using a tuning fork of frequency $256 \, \text{Hz}$, the first resonance position was $35 \, \text{cm}$, and the next position was $100 \, \text{cm}$. Calculate the velocity of sound in air.

    (c) (i) State the three classifications of musical instruments.
    (ii) Give one example of each classification.

    (d) Calculate the critical angle for light traveling from glass to air. [Refractive index of glass = $1.5$].
    (e) The speed of sound in a medium at a temperature of $102^\circ \text{C}$ is $240 \, \text{ms}^{-1}$. If the speed of sound in the medium is $310 \, \text{ms}^{-1}$, calculate its temperature.

11. (a) State two factors that affect the rate of evaporation of a liquid.
    (b) Explain the term latent heat.
    (c) Explain each of the following:
    (i) On a dry day, water in a clay pot is cooler than water in a rubber container.
    (ii) Cooking food is faster in a pressure cooker than in an ordinary pot.

    (d) A $40 \, \text{V}$ electric heater supplies a current of $12 \, \text{A}$ for $1400 \, \text{s}$ to a body of mass $1.5 \, \text{kg}$ at its melting point. The body melts, and its temperature rises by $60^\circ \text{C}$ in an additional $1.2 \, \text{min}$. Calculate:
    (i) The latent heat of fusion of the body.
    (ii) The specific heat capacity of the body.

    (e) State two differences between evaporation and boiling.

12. (a) (i) What is artificial radioactivity?
    (ii) Complete the table below:

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(b) In an X-ray tube, an electron is accelerated from rest towards a metal target by a \( 30 \, \text{kV} \) source. Calculate the kinetic energy of the electron. [\( e = 1.6 \times 10^{-19} \, \text{C} \)].  

(c) The table below shows the frequencies of radiations incident on a metal and the corresponding kinetic energies of the photoelectrons:  

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    (i) Plot a graph of kinetic energy (\( K.E. \)) against frequency (\( f \)).  
    (ii) From the graph, determine:  
    - Planck's constant.  
    - Threshold frequency.  
    - Work function of the metal.