In his first attempt, a long jumper took off from the spring board 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 \(\frac{u^2 sin 2\theta}{g}\) where all the symbols have their usual meanings, show that he gains a distance of 0.8576 m in his second attempt. [g = 10ms\(^{-2}\)]

The diagram above illustrates the path ABC, in a vertical x z plane, of a bullet shot into the air at an angle above the horizontal. Copy the diagram, and, using arrows, indicate the relative magnitudes and directions of the vertical and horizontal components of the velocities of the bullet at the point A, B and C.

(a) For a water voltameter, identify the;

(i) electrolyte;

(ii) electrodes;

(iii) substances deposited on the electrodes

(b)State the ratio of the volume of the substances deposited in (a) (iii) above

A parallel beam of unpolarised light is incident on a plane glass surface at an angle of 58\(^{o}\) to the normal. If the reflected beam is completely polarised, calculate the refractive index of the glass.