Projectiles (2)

Object projected at an angle A to the horizontal
(a) Range
Range (R) = horizontal velocity x time = [ucos A x 2u sin A]/g = [u²2 sin A cos A]/g

Range (R) = u²sin 2A/g

The maximum range for a given velocity of projection will be when sin 2A = 1, that is, when 2A = 90^o or when A = 45^o

(b) Height
The projectile will reach its maximum height when the vertical component of its velocity is zero, that is, when u sin A - gt = 0, or when t = u sin [A/g]

Maximum height (H) = [u²sin²A]/2g