A plane flies horizontally at an altitude h = 4 km with a horizontal speed of 540 km / h ; it launches , without speed relative to the plane , a bomb . The pilot intends to bombard an immobile target , ahead on the ground . To study the motion of the bomb , we consider the system ( XOy ) of origin 0 representing the position of the plane at the instant of launching of the bomb as shown in the adjacent figure . We neglect air resistance . Given g = 9.8 m / s ? 1 ) Determine the launching speed of the bomb .
2 ) Determine the parametric equations of motion of the bomb .
3 ) At what distance « d » from the target should the pilot launch the bomb ?
4 ) Determine the direction and the magnitude of the velocity vector of the bomb at the point of impact with the target
5 ) Determine the position of the plane at the instant of hitting the target .
6 ) Precise , with justification , the trajectory of the bomb with respect to the pilot