Question

A ball is thrown vertically upwards with a velocity v and an initial kinetic energy E_k. When half way to the top of its flight, it has a velocity and kinetic energy respectively of

(A) v/2, E_k/2

(B) v/√2, E_k/2

(C) v/4, E_k/2

(D) v/2, E_k/√2

(E) v/√2, E_k/√ 2

Answer 1

Correct option (B) v/√2, E_k/2   

Half way up you have gained half of the height so you gained ½ of potential energy. 

Therefore you must have lost ½ of the initial kinetic energy 

so E₂ = (E_k/2).

Subbing into this relationship E₂ = (E_k/2) 

½ mv₂² = ½ mv²/ 2

v₂² = v²/2 …. Sqrt both sides gives answer