How was w (weight) eliminated from this equation? how is 1/2wv^2/g equal to v^2/2g?
bernoulli’s equation
z + p/ρg + v^2/2g = constant
v2/2g term has square of velocity in numerator which hints of the kinetic energy. but as we know kinetic energy is ½ mv^2 so the third term in the bernoulli’s equation is the kinetic energy per unit weight. mass ‘m’ can be written as w/g so ½ mv^2 is equal to ½ wv^2/g or v^2/2g. it has the dimensions of nm/n or m, the kinetic energy per unit weight of fluid particle, which is also called velocity head.

Samir watches a 100-minute movie on his spaceship. maria's spaceshipe flies in the same direction as samir's spaceship but she observes his move to last 125 minutes and his spaceship to be 40 m long. how long does samir observe his own spaceship to be? according to an observer on earth, planet x is stationary. maria and samir depart earth on their spaceships at the same time, each flying at 0.5c. maria flies toward planet x and samir flies in the opposite direction. according to maria, her voyage to planet x takes 9 years. how many years does marias voyage take according to samir?

If the force applied to an object remains constant, is more power needed for the object to move faster ? explain

Two resistors r1 and r2 may be connected either in series or parallel across an ideal battery with emf ε. we desire the rate of energy dissipation of the parallel combination to be 8.75 times that of the series combination. if r1 = 105 ω, what are the (a) smaller and (b) larger of the two values of r2 that result in that dissipation rate?