The trajectory of a projectile in a vertical plane is given by the equation y = x - x^2 , where and are positive constants, and x and y are the horizontal and vertical distances from the point of projection, respectively. The ratio of the maximum height attained by the projectile to its horizontal range is

Step-by-step solution

The standard equation of trajectory for a projectile is given by: y = x - g x^2 2 u^2 ^2 Comparing this with the given equation y = x - x^2 , we get: = The horizontal range R and maximum height H are given by: R = u^2 2 g = 2 u^2 g H = u^2 ^2 2g The ratio of maximum height to horizontal range is: H R = u^2 ^2 2g 2 u^2 g = 4 Substituting = , we get: H R = 4 Answer: 4