(a) In his first attempt, a long jumper took off from the springboard with a speed of 8 ms\(^{-1}\) at 30° to the horizontal. He makes a second attempt with the same speed at 45° to the horizontal. Given that the expression for the horizontal range of a projectile is \(\frac{v^2 sin \theta}{g}\) where all the symbols have their usual meanings, show that he gains a distance of 0.8576 m in his second attempt.

(b)(i) State Hooke's law of elasticity.

(ii) Describe an experiment to verify Hooke's law.

(iii) State two precautions you would take if you were to perform this experiment in the laboratory.

(c) A spiral spring of natural length 20.00 cm has a scale pan hanging freely in its lower end. When an object of mass 40 g is placed in the pan, its length becomes 21.80 cm. When another object of mass 60g Is placed in the pan, the length becomes 22.05cm. Calculate the mass of the scale pan. [g = 10 ms\(^{-2}\)]

(a) Define specific heat capacity.

(b)(i) With the aid of a labelled diagram, describe an experiment to determine the specific heat capacity of copper using a copper ball.

(ii) State two precautions necessary to obtain accurate results.

(c) A piece of copper block of mass 24 g at 230°C is placed in a copper calorimeter of mass 60 g containing 54 g of water at 31°C. Assuming heat losses are negligible, calculate the final steady temperature of the mixture. [specific heat capacity of water = 4200 J kg\(^{-1}\) K\(^{-1}\)] [specific heat capacity of copper = 400 J kg\(^{-1}\) K\(^{-1}\)]

(a)(i) What is an echo? (ii) State two useful applications of echoes.

(iii) Why are the walls, floors and ceilings of a recording studio heavily padded?

(b)(i) Explain timbre and overtones.

(ii) What is resonance?

(c) As a ship approaches a cliff, its siren is sounded and the echo is heard in the ship after 12 seconds. 2.1 minutes later the siren was sounded again and the echo was heard 8 seconds later. If the speed of sound in air is 340 ms\(^{-1}\), calculate the velocity at which the ship was approaching the cliff.

(a) Explain the statement the capacitance of a capacitor is 5\(\mu\)F.

(b)(i) State the factors upon which the capacitance of a parallel plate capacitor depend.

(ii) State how the capacitance depends on each of these factors stated in (b)(i).

(c) A series arrangement of three capacitors of values 8uF, 12\(\mu\)F, and 24\(\mu\)F is connected in series with 90-V battery.

(i) Draw an open-circuit diagram for this arrangement.

(ii) Calculate the effective capacitance in the circuit.

(iii) On closed circuit, calculate the charge on each capacitor when fully charged.

(iv) Determine the p.d across the 8\(\mu\)F capacitor.

(a) When nitrogen (atomic mass = 14, atomic number = 7) is bombarded with neutrons, the collisions result in disintegrations in which alpha particles are produced. Represent this transmutation in a symbolic equation.

(b)(i) How does a radioactive atom differ from a stable one?

(ii) Explain 'half life'.

(iii) A sample of radioactive material has a haft life of 35 days. Calculate the fraction of the original quantity that will remain after 105 days.

(c) Light of wavelength 5.00 x 10\(^{-7}\)m is incident on a material of work function 1.90 eV. Calculate

(i) photon energy.

(ii) kinetic energy of the most energetic photo electron.

(iii) stopping potential [Plancks constant h =6.6 x 10\(^{-34}\)Js] [c= 3.0 x10\(^8\)ms\(^{-2}\), leV= 1.6 x 10\(^{19}\)J]