# Two Dimensional Motion

## What is Projectile Motion?

 ~Galileo Galilei~ Image courtesy of Famous Scientists

Throw a ball at an angle up off a building. It is now a projectile, which is an object that is propelled by another force and continues to travel because of its own inertia. Watch at first as it travels at the angle that you threw it. When the ball’s velocity reaches zero, (which is its highest point), it begins to travel down to the ground while moving horizontally because its force is constant. This is an example of Projectile Motion. Projectile Motion is a nonlinear motion in which matter travels on a curved path or motion under the influence of gravity. In the late 1500s a famous physicist, Galileo Galilei, was the first to accurately describe projectile motion and showed how the motion had seperate components such as constant horizontal motion and the object would continue to accelerate downward because of gravity. Inertia is a large part of projectile motion because it explains precisely why an object continues to be in motion even after a force has stopped being exerted on it. 3 4

## Vector Quantities, Scalar Quantities, and Velocity Vectors

Scalars and vectors are used to describe the magnitude and or direction of a specific quantity. To show how much an animal weighs you would define it by a scalar quantity. A Scalar quantity is a quantity that is only described by magnitude. This includes quantities such as time and volume. An Example for volume is the amount of water in an aquarium is scalar because it is a single number and does not have more than one number associated with it. More examples are temperature, mass, and population of a city; are all scalar because they will be defined with one number. To model an object that is traveling in a specific direction, you would use something callled vector quantity. Vector quantity requires both magnitude and direction for a complete description. Examples of this is an airplane flying at the speed of sound. This is not completely defined because we do not know in what direction the jet is travelling. Say the jet is traveling 80 degrees east; this then would be considered a vector because the quantity is associated with more than one number.

Velocity is used to describe the speed and direction of a object and velocity vectors are used to determine the exact velocity of an object, including any other velocities that may interfere with the object. Suppose that a bird is flying at 25mph north and there is gust of wind blowing at five mph north. To show the bird’s speed a vector would be a certain length, drawn to scale. To show the direction the vector would simply be pointing north. If a figure were to show this, it would be somthing like each centimeter represents five mph. So the a bird speed is shown by the vector pointing north that is 5cm long and the tailwind is shown by the vector one centimeter long, pointing north. So this would simply show that the bird’s actual velocity is 30mph. If instead there was a headwind 10mph south and not a tailwind it would be shown as a vector pointing south, two centimeters in length. 1 2 910

## Projectile Motion

Projectile motion is simply any object that is propelled by a force into the air. The path of a projectile under only the influence of gravity is known to be parabolic arc, which is a curved path who's midpoint is equidistant from either end. After an object has been launched its inertia helps the object travel upwards but eventually it will fall back down to earth. This is because of the only constant force in projectile motion, gravity. Gravity pulls the object down before and after the object loses its inertia. If there was not any gravity the object would travel in a straight line because of the no existent downward force. When an object is launched it usually has both horizontal and vertical movement, i e , it doesn't move simply horizontally or vertically but in an arc. The vertical and horizontal components act independently to cause the projectile to travel in a parabolic path. Because Gravity works only in one direction, down, it affects only one facet of projectile motion, the vertical. The downward force of gravity is always the same even if there is a horizontal movement of the object. This means that a projectile moving horizontally, no matter how fast, will hit the ground in the same time it takes an identical object tio merely fall from the same starting height. This also means that an object moving in a parabolib arc hits the ground with the same velocity it began with. In projectile motion, any forces act independently from one another.5 6 11 [10]

## Earth Satellites

Satellites are objects the orbit the earth, such as our Moon or man-made satellites. If you shot a cannon ball horizontally, it would fall at an acceleration of approximately 10 meters per second towards the ground due to gravity. If shot horizontally, the distance fallen vertically stays the same no matter how fast it may travel, but if you shoot the cannon ball fast enough, neglecting air resistance, the cannon ball can very well orbit the earth. If an object is sent at 8000 m/s, it would travel fast enough to fall and miss the earth and remain in orbit traveling in a circular path, but anything over 8000 m/s will orbit in an elliptical path since it is closer to breaking Earth's gravitational pull altogether. Most people believe that artificial satellites are sent in to orbit around earth not experiencing any gravity form earth. In fact at even 150 kms the effect of gravity is much the same as on Earth. Since this is so, the reason that satellites do not come crashing down is that they are moving so quickly that they constantly overshoot the surface. Put differently, orbit is merely the act of constantly falling around an object.

## References

1. Vectors: Velocities,