To find the horizontal range R of a projectile, the equation R = vt cos is

To find the horizontal range R of a projectile, the equation R = vt cos α is used, where α is the angle between the line of fire and the horizontal, v is the initial velocity of the projectile, and t is the time of flight. It can be shown that t = (2v sinα)/g, where g is the acceleration due to gravity. Show that R = (v²sin 2α)/g. See Fig. 20.19.

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Fig. 20.19 R