# E103 Projectile Motion

Physics is not all about the Resolution of Forces and Kinematics. One of the topic in Physics is Projectile Motion. Projectile Motion is a special case of two-dimensional motion. Gravity is the only considered external force acting on it while an object is airborne. Projectile is the moving body in this kind of motion. It refers to any object thrown, launched or otherwise projected so that once released, if air resistance is neglected, its path is affected only by the Earth’s gravity. As fired at an angle, it is influenced by its horizontal inertia and vertical gravity. The projectile creates a parabolic curve. The curved path is known as the trajectory. We are assuming here that there is no or very little air resistance. The equations of motion for one dimension are also valid for two dimensions. To simplify our analysis, we will resolve the position, velocity, and acceleration into horizontal and vertical components. Because these components are perpendicular, they are independent to each other.

In this experiment, you will analyse the motion of a projectile. Specifically, you will be able to explain the effects of variable launch angles and initial speeds to the positions of the projectile along the x-axis and y-axis. The objective of this experiment is to analyse the motion of projectile and to compare the ranges of projectiles launched at different angles. In this, the explanation on the effects of variable launch angles and initial speeds to the positions of the projectile along the x-axis and y-axis will be obtained. The restrictions of this experiments is to never aim the projectile launcher to any person or breakable objects and to make sure that the launcher’s base is securely clamped to the iron stand. From Newton’s first Law of Motion, it states that an object will continue to a straight line with constant velocity if there is no external factor that will cause its stop or change its direction. If an object is fired in horizontal orientation, the object will go in to the direction perfectly with constant velocity. It is also called the “free-way path.” It is shown in Figure 1.

Figure 1. Free-way Path

As to consider gravity as external force acting on the object and a factor to change the state of the object, the motion creates a trajectory or simply a projectile motion. Since gravity is force downward, the object fired on the straight line or in angle, ϴ, will tend to go to the direction of the force, downward just as shown in Figure 2.

Figure 2

The trajectory made by the projectile is a parabolic curve. Considering the only force acting on the object is gravity, the object slows as it approaches the peak or the maximum height or when velocity is equal to zero. It starts to go down because gravity affects the vertical terms of the projectile. In the absence of force in horizontal terms, the velocity in horizontal direction is constant. To aid visualization, see Figure 3. Figure 3

As said earlier, the three kinematic equations in one-dimensional motion is also applicable in two dimensions. Those are velocity as a function of time (1), position as a function of time (2) and velocity as a function of position (3). Then, from these equations, we can derive the equations for projectile motion as shown in Table 1. (1)

(2)

(3)

Table 1. Equations for Projectile Motion

x-axis

y-axis

acceleration

0

a=-9.8m/s2

velocity

vx=v0cosϴ

vy=v0sinϴ

position

x=x0+ v0cosϴt

y=y0+ v0sinϴt+1/2(gt2)

In this experiment, we used a projectile launcher (Fig. 4), an iron stand with clamp, and target board (Fig. 5), a metal ball and a plumb line (Fig. 6), a meter stick and projectile launcher’s rod (Fig. 7). We also used bond papers and carbon paper to determine where the metal ball will fall. To avoid inaccuracy, we put a lot of tape on the projectile launcher and also on the papers. We are going to observe the trajectory of the...

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