Applications of Projectile Motion

Projectile Motion, by definition, is the motion of an object thrown or projected into the air, only subject to acceleration due to gravity. The motion has a constant horizontal velocity combined with a constant vertical acceleration caused by gravity. This is usually thought of as the motion of a ball thrown while playing catch, the arc of a basketball shot, or a kicked football trajectory.

However, there are many other instances where projectile motion is applicable, whether it is in daily life or in technological advancements. Here are some of the applications of projectile motion.

1: Sports

Projectile motion is very common in sports, since most sports involve the motion of a projectile (usually a ball). By using physics, we are able to determine the optimal angle of a ball’s flight in order to maximize speed or distance.

Baseball

Projectile motion is applicable in both throwing and hitting. A thrown ball undergoes projectile motion when it is mid-air since the only force that affects the ball is the acceleration due to gravity. Baseball analysts can analyze baseball pitchers using an understanding of kinematics and projectile motion. A variety of factors will go into the trajectory of a pitch, including a pitcher’s height, arm angle, and the spin being applied to the ball. All of these, along with kinematics, are used to determine how fast a pitch is being thrown relative to the batter’s eye. Typically, a 90 mph pitch takes 0.4 seconds to reach the batter from around 55 feet (subtracting the pitcher’s stride from the regular 60 feet); this can be calculated using kinematics.

In terms of hitting, advanced analytics like to use “launch angle” as a good indicator of the optimal angle that a ball should be hit. Launch angle is the angle at which a ball exits the bat as soon as they contact each other. The best launch angles, which allow for line drives and home runs, are calculated to be around 10–30 degrees North of East, relative to the bat. This allows for the most optimal ball flight, usually necessary to hit the ball over 325 to 400 feet over the fence.

Basketball

Another example of projectile motion in sports is in basketball. For a basketball shot to enter the hoop, the basketball must be shot at a certain angle with a certain amount of force. The optimal angle of a shot will vary depending on the height from which the ball is shot and the player’s distance from the hoop. According to Professor John Fontanella, the ideal angles from the free throw line will vary from 48.7 degrees to 52.2 degrees, with shorter players requiring a higher arching shot to compensate for the height difference of the initial release. This angle considers both the arc of the basketball and the force required to shoot the basketball. The higher the arc, the more room for error a shooter can have. However, a higher arc will require more force to allow the ball to reach the hoop. As well, the force of gravity will increase the speed of the ball as it falls. This is why you cannot simply shoot the ball with a near-vertical degree angle and expect more shots to drop in on top of the amount of strain you will put on your body by using more force to shoot each time.

2: Programming/Animation

Another example of the application of projectile motion is in programming. The challenge for modern-day programmers and animators is to model real-life physics as accurately as possible, whether for a tv show or a video game. Great video games attempt to follow them as accurately as possible, whether it is the physics of a baseball being hit or the physics of a person falling a certain height. For the games to be enjoyable, they must be as close to reality as possible; a golfing game would not be fun and realistic if the ball were being driven 1000 yards.

3: Other applications

Other examples where projectile motion may be applied to real-life are in certain appliances and the military. Looking at appliances at home, objects such as water hoses or water guns involve projectile motion. Instead of a ball, the “projectile” in question is water. However, it is still an object in the air, only affected by gravity when released, meaning it is considered projectile motion. The distance that the water will travel once it exits the hose depends on the hose’s angle and the force that the water is being exerted. The force that the water can exert is not very high for the product in hand to be safe and helpful in watering plants, so the distance that the water can travel is not very far. However, the angle of the hose can be changed to reach certain parts of the garden/soil. By optimizing the water’s launch angle (45 degrees), the water can travel as far as possible, minimizing the distance you need to walk to water your entire garden.

The military and the manufacturing of their weapons also involve projectile motion. A bullet, when shot from a gun, is considered a projectile in the air. The bullet will travel at a much higher speed than the water from the water hose, meaning it will travel a much further distance and will be less susceptible to acceleration due to gravity, relative to how much it travels horizontally. However, it is not like gravity is not affecting the bullet. Thus, manufacturers of guns attempt to maximize the speed that the bullet is released from the weapon while minimizing the gun’s amount of recoil. This would help soldiers maximize aim while reducing other factors that would cause them to be inaccurate.