Projectile motion can be defined as the motion of an object which is thrown or projected into the air, subject to only the acceleration of gravity. The object is known as a projectile, and the path is known as its trajectory. The motion of falling objects is an example of one-dimensional type of projectile motion in which there is no horizontal movement. In this section, two-dimensional projectile motion is considered, such as a football or other object in which air resistance is very less.
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The main point to be noted is that motions along perpendicular axes are independent and can be analyzed separately. The secret to understand two-dimensional projectile motion is to break it into two motions, one motion along the horizontal axis and the other motion along the vertical. The horizontal axis is called the x-axis and the vertical axis as the y-axis. Figure 1 demonstrates the notation for displacement, where s is the total displacement and x and y are its components along the horizontal and vertical axes, respectively. The magnitudes of these vectors are shown by s, x, and y.
To describe motion, velocity, acceleration, and displacement are dealt with. Their components are found out along the x- and y- axes. All forces are taken onto account except gravity.
Many things have to be understood well in order to get ‘projectile motion’. Most students try to cram up the equations. This is not at all a good strategy because it will be overwhelming to memorize all the equations and not know its proper usage.
Students face difficulties in projectile motion which is the first problem in two-dimensional motion. Thus, students try to manage both the horizontal and vertical motions of the projectile.
Another problem which students face is that it becomes difficult for them to separate the notion of acceleration from the notion of velocity.
The third problem is that these problems are discussed prior to discussing how forces affect the motion of objects. If a student already knows that forces cause objects to accelerate and they accelerate in the same direction like the force, then it will be not hard to understand that the only force on a projectile when in motion is the gravitational force. Also, the force occurring due to gravity is always vertically downward. That is why it is important because it tells that the vertical motion of a projectile is the only part which has acceleration. Thus, regardless of the horizontal speed at the initial stages, it will not change until the projectile hits the ground. This will make you separate the vertical motion- that is the y-motion – from the horizontal or x-motion. This will simply the problem.
So, projectile problems become easier if one realizes that the vertical motion is identical to any free-fall problem which can be understood with a ball thrown straight up in the gravitational field and then observe how high it goes and for how long it stays in the air before it hits the ground. If a student can do that problem, then he or she will also be able to solve projectile motion problems.
Then it is observed that in the horizontal direction, there is no force once it is on its way. So long as it is in the air, it is traveling horizontally at a constant speed.
Combining all these ideas will help to see how high it will go, how far it had travelled when it reaches its maximum height, how long it will remain in the air, and how far it travels horizontally before hitting the ground.
Students’ misconceptions about projectile motion
The concept of force
A sound knowledge is necessary in order to know Galileo’s method of decomposing motion into horizontal and vertical components. Some ideas which students have regarding force are:
- When an object is at rest, then there are no forces acting on it.
- When an object is moving, then there must be a force in the direction of motion.
- Force is a kind of energy which causes the motion and at the same time, it is consumed by the motion itself. This was the idea of John Philoponus.
- When force increases, then speed also increases.
Students are also not very clear about the nature of gravity just as Galileo had problems. Some of the beliefs by the students are:
- When an object is lying on the ground, then gravity is not acting on it because it has already fallen on the ground.
- Gravity happens as a result of air pressure.
- Gravity is a one of the properties of the object.
- The objects which fall have more gravity than the stationery objects or there is no gravity exerted on stationery objects.