Projectile motion

Projectile motion is a special case of two dimensional motion with constant acceleration. Here, force due to gravity moderates linear motion of an object thrown at certain angle to the vertical direction. The resulting acceleration is a constant, which is always directed in vertically downward direction.

The projectile motion emphasizes one important aspect of constant acceleration that even constant acceleration, which is essentially unidirectional, is capable to produce two dimensional motion. The basic reason is that force and initial velocity of the object are not along the same direction. The linear motion of the projected object is continuously worked upon by the gravity, which results in the change of both magnitude and direction of the velocity. A change in direction of the velocity ensures that motion is not one dimensional.

The change in magnitude and direction of the velocity is beautifully managed so that time rate of change in velocity is always directed in vertically downward direction i.e. in the direction of gravity. This aspect is shown qualitatively for the motion in the figure below as velocity change successively at the end of every second from $v_1$ to $v_2$ to $v_3$ and so on….. by exactly a vector, whose magnitude is equal to acceleration due to gravity “g”.

Force(s) in projectile motion

Flight of base ball, golf ball etc. are examples of projectile motion. In these cases, the projectile is projected with certain force at certain angle to vertical direction. The force that initiates motion is a contact force. Once the motion of the ball is initiated, the role of contact force is over. It does not subsequently affect or change the velocity of the ball as the contact is lost.

In order to emphasize, we restate three important facts about projectile motion. First, we need to apply force at the time of projection. This force as applied by hand or by any other mechanical device, accelerates projectile briefly till it is in contact with "thrower". The moment the projectile is physically disconnected with the throwing device, it moves with a velocity, which it gained during brief contact period. The role of force responsible for imparting motion is over. Second, motion of projectile is maintained if there is no net external force (Newton's laws of motion). This would be the case for projection in force free space. The projectile is initiated into the motion with certain initial velocity, say u . Had there been no other force(s), then the ball would have moved along the dotted straight line (as shown in figure below) and might have been lost in to the space.

Third, the projectile, once out in the space, is acted upon by the force due to gravity and air resistance. We, however, neglect the effect of air resistance for the time being and confine our study of the motion which is affected by force due to gravity acting downwards. The motion or velocity of projectile is then moderated i.e. accelerated (here, acceleration means change of speed or change of direction or both) by gravity. This is the only force. Hence, acceleration due to gravity is the only acceleration involved in the motion. This downward acceleration is a constant and is the acceleration in any projectile motion near Earth, which is not propelled or dragged.