question_answer 32)

(a) Show that for a projectile the angle between the velocity and the X-axis as a function of time is given by   (b) Show that the projection angle  for a projectile launched from the origin is given by:   where the symbols have their usual meaning.  

Answer:

(a) As shown in Fig. 4.111, suppose the projectile is thrown with a velocity  at an angle  with the X-axis. Fig. 4.111   Let  and  be the components of velocity  along X- and Y-directions respectively. At any time t, suppose the particle is at point P. Its velocity  has components  and  along X- and Y-directions. Then         [Horizontal component and                remains unchanged] If the velocity v makes angle  with X-axis, then     (b) Maximum height attained by the projectile   Horizontal range of the projectile,               or     Hence, .