# Projectile Motion

Throwing a ball vertically upward, we can catch it right back to our hand. The ball leaves our hand. Then it reaches the highest point. It comes back to our hand, exactly on its initial place. In other case, throwing the ball at a certain angle with the horizontal, we can’t catch it back. The later is an example of projectile motion.

Projectile motion is a motion whose path is parabola shaped. It comprises of two parts of motion. They are perpendicular each other. The first is uniformly horizontal motion. The second is uniformly accelerated vertical motion. For a body moves a projectile motion, one has to give motion in these two directions on it simultaneously.

Uniformly accelerated motion means motion with a constant change of velocity. In the vertical direction, the thrown object undergoes a force. This force is due to the Earth’s gravitational field. We name the strength of this field as gravitational acceleration. It slows down the object during its ascending motion. At a time, the object lost all of its velocity. It stays at rest for a short moment. The force of gravity is still there. Then, the object starts to carry on its descending part. This is what happens in vertically upward motion. The ascending time equals to the descending time.

In addition to the vertical movement, projectile motion also has horizontal movement. The velocity remains constant during this motion. How come this horizontal movement occurs? This occurs when we throw the object making an angle with the horizontal. The object has horizontal velocity component. This horizontal velocity doesn’t undergo acceleration. No force acting in horizontal direction. We neglect the small air resistance. The horizontal distance travelled is constant.

There are two important things in projectile motion. The first is the constant distance travelled in the horizontal direction. The second is the varying distance travelled vertically. The combination of them makes the parabola trace in projectile motion. What if the distances travelled in both directions are constant? The trace of the motion will be a straight line. What if both of them are varying? The trace can be a circle or ellipse shaped. It depends on the acceleration in each direction.

What do affect the highest point can be reached in projectile motion? There are three quantities. The first is the initial velocity. The second is the angle of this velocity with the horizontal. I will call it initial angle from now and on. The last is the gravitational acceleration. The product the initial velocity and the sinus of the initial angle are called the vertical component of the initial velocity. Simply call it vertical velocity. The greater the vertical velocity the higher the object climbs up. The highest point also determined by the gravitation acceleration at that place. The greater the acceleration, the less the highest point can be reached.

What do affect the horizontal distance travelled by a projectile motion then? Similarly, it is determined by the initial velocity, initial angle, and the gravitational acceleration. This time, the horizontal component of the initial velocity also takes its part. I will call it horizontal velocity. The vertical velocity affects the time of motion. The horizontal distance travelled is the product of the horizontal velocity and the time of motion. The longer the time of motion, the further the horizontal distance will be.

Athletes of discuss throwing, javelin throwing, long jump etc make benefit by understanding this projection motion calculation. In order to get the best result, they take an angle about 45 degrees from the horizontal when they throw, jump or something. This angle will give the furthest distance for a certain initial velocity. The velocity resulted by the athletes is constrained by their power. They have to use it effectively to beat their competitors. The parameters can be manipulated is the angle. They practice to be familiar with this angle of jump or throw.

Many other things exhibit projectile motions. Here are examples to help you to figure it out. The bombs released from the bomber planes move in projectile path. The horizontal velocity equals to that of the plane. The ball thrown by the basket ball player demonstrates this. The stone thrown from the catapult also demonstrates projectile motion. Water from the waterfall makes a projectile motion.

Projectile motions frequently occur around us. It is important for us to understand it. We take many benefits of it. Thank God for His Creations.