The maximum vertical distance attained by the projectile is called maximum height. In P motion one may wish to determine the height to which the projectile rises, the time of flight and horizontal range. The angle Φ which this resultant velocity makes with the horizontal can be found from: The magnitude of velocity at any instant is:
By using the first equation of motion (V f = V i + at) the vertical component V fy of the velocity at any instant t is given by: The initial vertical component of the velocity is V sinθ in the upward direction. Hence, the horizontal component V x remains constant and at any time t, we have: The horizontal acceleration is ax = 0 because we have neglected air resistance and no other force is acting along with the direction resistance and no other force is acting along this direction whereas vertical acceleration a y = g. Suppose that a projectile is fired in a direction angle θ with the horizontal by velocity V along the horizontal and vertical components of velocity V along the horizontal and vertical directions be V cosθ and V sinθ respectively. In such cases, the motion of a projectile can be studied easily by resolving it into horizontal and vertical components that are independent of each other. A football kicked off by a player a ball thrown by a cricketer and a missile fired from a launching pad, all projected at some angles with the horizontal, are called projectiles. It is not necessary that an object should be thrown with some initial velocity in the horizontal direction.
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