The equation of trajectory of a projectile is given by y = x - 5x^2 , where x and y are the horizontal and vertical displacements respectively, measured in meters. The maximum height attained by the projectile is:

Step-by-step solution

The equation of the trajectory is y = x - 5x^2 . The maximum height corresponds to the maximum value of the vertical displacement y . To find the maximum value of y , we differentiate y with respect to x and set it to zero: dy dx = 1 - 10x = 0 10x = 1 x = 0.1 ~m This means the projectile reaches its maximum height at a horizontal distance of x = 0.1 ~m . To find the maximum height, substitute x = 0.1 ~m back into the trajectory equation: y_ max = (0.1) - 5(0.1)^2 y_ max = 0.1 - 5(0.01) y_ max = 0.1 - 0.05 = 0.05 ~m