In order to determine the kinetic energy of an explosion it is necessary to know the initial velocities of ejected fragments. Calculations of initial velocities made earlier with few exceptions did not take into account the resistance of the air and therefore, greatly underestimated the initial velocities, and consequently the energy of the explosions. A solution of the inverse problem of ballistics which takes into account air resistance makes it possible to find precise values of initial velocities of ejection, determined from the distance of ejected fragments and their ballistic coefficients. The method makes it possible to determine the kinetic energy of explosions for eruptions which were not directly observed. It is shown that the velocity field in volcanic explosions is not spherical,i.e. the velocities of ejection of fragments differ markedly in different directions. Accordingly, the maximum distance of ejection of fragments depends not only on the initial angle of ejection, but also on the character of distribution of initial velocities and the ballistic coefficients of the fragments. For fragments with diameters of 40 cm to 2 m the maximum distance of ejection is realized in the case of angles of ejection of 30–36°. For smaller fragments the optimal angles of ejection are still smaller. The ballistics of explosive eruptions of the volcanoes Asama, Arenal, and Shiveluch are considered.