A stone is projected vertically upwards with speed ' v '. Another stone of same mass is projected at an angle of 60^ with the vertical with the same speed ' v '. The ratio of their potential energies at the highest points of their journey is [ 30^ = 60^ =0.5 . , . 30^ = 60^ = 3 2 ]

Step-by-step solution

P.E. of the stone projected vertically is, P.E. = mgh But h = v ^2 2 ~g aligned P. E ₁ & = mg ( v ^2 2 ~g ) & = mv ^2 2 ... (i) aligned For the second stone thrown at an angle to the horizontal, array ll & h = v ^2 ^2 2 ~g = v ^2 ^2 30^ 2 ~g = v ^2 8 ~g & P.E. 2= mg ( v ^2 8 ~g )= mv ^2 8 ... (ii) array Dividing equation (i) by equation (ii) - - P E₁ P E₂ = ( m v^2 2 ) ( m v^2 8 ) =4: 1