A body of mass (m) is theown with velocity (u) at an angle ` 30^(@)` to the horixontal and another body ` B` of the sme mass is thrown with velocity (u) at an angke if `45&(@)` to the horizontal, find the ration of the horizontal range and max. height of ` A and B` .

Explanation

Case(i) Whe ` theta =30^@ ` ,
` R_A = u^2 /g sin 2 xx 30^@ = u^2 /2 xx (sqrt3)/2 ,
`H_A = u^2 /(2 g) sin^2 30^@ = u^2/ (2 g) xx 1/4 = u^2/(8 g)`
Case (ii) When ` theta = 45^@ ,
` R_B = u^2 /(2 g) sin ^2 45^@ = u^2 /(2 g) xx 1/2 =u^2/g ,
` H_B = u^2 /g sin 2 xx 45^@ = u^2/ 2 g) xx1/2 = u^2/ (4 g)`
:. ` R_A : R_B = sqrt 3 : 2 and H_A : H_B =1: 2.