Two projectiles A and B are thrown with the same initial kinetic energy. The mass of projectile A is m and the mass of projectile B is 2m . If projectile A is thrown at an angle of 30^ with the horizontal and projectile B is thrown at an angle of 45^ with the horizontal, the ratio of their horizontal ranges R_A : R_B is

Step-by-step solution

The kinetic energy of a projectile is given by K = 1 2 m u^2 . Given that the initial kinetic energies are equal ( K_A = K_B ): 1 2 m_A u_A^2 = 1 2 m_B u_B^2 1 2 m u_A^2 = 1 2 (2m) u_B^2 u_A^2 = 2 u_B^2 The horizontal range is given by R = u^2 (2 ) g . For projectile A ( _A = 30^ ): R_A = u_A^2 (60^ ) g = 2 u_B^2 g 3 2 = 3 u_B^2 g For projectile B ( _B = 45^ ): R_B = u_B^2 (90^ ) g = u_B^2 g 1 = u_B^2 g The ratio of their horizontal ranges is: R_A R_B = 3 u_B^2 g u_B^2 g = 3 1 Thus, R_A : R_B = 3 : 1 . Answer: 3 :