Projectile Motion

• Projectile motion is the movement of a body through the air following a curved flight path under the force of gravity.
• Projectile: a body that is launched into the air losing contact with the ground surface.
• There are four factors that affect the horizontal distance travelled by a projectile: speed of release, angle of realease, height of release, and aerodynamic factors.
• Speed of release: due to Newton's second law, the greater the outgoing speed of the projectile, the further it will travel.
• Aerodynamic factors: Bernoulli and Magnus.
• When height of release is equal to the landing height, the optimal angle of release is 45º
• When height of release is above landing height, the optimal angle of release is below 45º
• When height of release is below landing height, the optimal angle is above 45º
• As height of release increases, the horizontal distance travelled increases.
• A parabolic flight path is a symmetrical flight path.
• A non-parabolic flight path is a asymmetrical flight path.
• A shot put is an example of a parabolic flight path.
• A badminton shuttle is an example of a non-parabolic flight path.
• If weight is the dominant force and air resistance is very small, a parabolic flight path occurs.
• A shot put follows a parabolic flight path becasue W>AR. Weight is high because mass is high. Air resistance is low because velocity is low and the shot put has a smooth surface.
• If air resistance is the dominant force and weight is very small, a non-parabolic flight path occurs.
• A badminton shuttle follows a non-parabolic flight path because AR>W. Air resistance is high because velocity is high and the shuttle does not have a smooth surface. Weight is low because mass is low.
• In a badminton shuttle, the air resistance appears to shorten the pre-determined flight path of the shuttle.
• Once a projectile is in flight additional lift forces (Bernoulli principle) can act on the body which can also extend the flight path making it non-parabolic.
• The additional bernoulli lift force extends the flight path so greater distances can be achieved.
• Spin could also be placed on the body such as top spin in tennis or backspin in golf which can also impact the pre-determined flight path due to Magnus force.
• Top spin decreases horizontal distance.
• Back spin increases horizontal distance.
• As the effect of air resistance increases, the more a projectile will deviate from a true parabolic flight path.
• Projectiles that travel at a very high velocity are most affected by air resistance and therefore follow a non-parabolic flight path.
• Projectiles that have a large frontal cross-sectional area are most affected by air resistance and therefore follow a non-parabolic flight path.
• Projectiles that don't have a smooth surface are most affected by air resistance and therefore follow a non-parabolic flight path.
• Projectiles that have a low mass are most affected by air resistance and therefore follow a non-parabolic flight path.
• The greater the mass of the projectile the longer the length of the weight arrow.
• The greater the frontal cross-sectional area/roughness of surface/velocity of the projectile the longer the length of the air resistance arrow.
• At the start of flight of a badminton shuttle, air resistance is much larger than weight, as the velocity of the shuttle is high as it leaves the racket head.
• During the flight of a badminton shuttle, the size of the air resistance force has decreased as the velocity of the shuttle has reduced. It is the size of the air resistance force itself that causes the shuttle to decelerate.
• At the end of the flight of a badminton shuttle, the air resistance force is now small as the velocity of the shuttle has slowed. The weight force has remained the same throughout the flight and is now larger than air resistance. Consequently, the shuttle falls vertically, resulting in a non-parabolic flight.
• Weight and air resistance should originate from the centre of mass of the projectile.
• Weight should act vertically downwards.
• Air resistance should act opposing the direction of motion.
• Free body diagrams should always have a direction os motion arrown.
• To consider the result of all forces acting upon a projectile in flight, a parallelogram of forces can be drawn. This diagram shows the resultant force acting on the projectile.
• A parallelogram of forces is created by drawing a free body diagram showing the forces of weight and air resistance.
• A parallelogram of forces is created by adding a broken parallel lines to weight and air resistance arrows to create a parallelogram.