A projectile is fired from the ground such that its horizontal range R is n times its maximum height H . If the total time of flight of the projectile is T , the horizontal component of its initial velocity is :

Step-by-step solution

Let u_x and u_y be the horizontal and vertical components of the initial velocity respectively. The horizontal range is given by R = 2 u_x u_y g . The maximum height is given by H = u_y^2 2g . According to the given condition, R = nH . Substituting the expressions for R and H : 2 u_x u_y g = n ( u_y^2 2g ) Simplifying this, we get: 4 u_x = n u_y The total time of flight is given by T = 2 u_y g , which gives u_y = gT 2 . Substituting the value of u_y into the previous relation: 4 u_x = n ( gT 2 ) u_x = n g T 8 Answe