Using lorentz transformations, verify that the space-time interval as an invariant quantity (i. e., show that its value does not change in different frames of reference).

No it doesnt because it can be any number.

Answer(b) both involve the use of levers;

At maximum height, kinetic energy is converted in potential energy  formula: at max height, ke = ½ * 0.27kg * (16m/s) ² = 34.56 j  so the remaining pe = (41.70 – 34.56)= 7.14 j = 0.27 kg * 9.8m/s² * h  = (9.8/7.14 * 0.27)so max height h = 5.08 or 5 m 

Electricity and discharge