## Physics Tutorial

#### Intro

Projectile motion is one of the keys concepts in physics and can be defined as 2-dimensional kinematic motion in which an object is launched at a certain angle giving the object motion in both the x and y directions. These problems are important to physics because they encapsulate concepts from kinematics and a key concept of dynamics, thus bringing together the two fundamental fields of classical mechanics. One of the toughest parts of projectile motion is understanding how the motion in the x and y directions are unique and independent from each other.

#### Sample Problem

Two balls are set up on a table at a height of 5 meters. Ball 1 has a mass of 2 kg, and ball 2 has a mass of 10 kg. Simultaneously, ball 1 is dropped directly down from that height, and ball 2 is pushed off of the table horizontally. Assuming friction and air resistance are negligible, which ball will hit the ground first and why?

They will hit the ground at the same time

It is impossible to determine without the force applied to ball 2

Ball 1 because it has less mass than ball 2

Ball 1 because it travels a less total distance in the air

Ball 2 because it has greater mass than ball 1

#### Solution

The correct answer is “They will hit the ground at the same time”.

One of the major concepts within projectile motion is the independence of the x and y components of motion. We can use our knowledge of forces to justify this claim. Since force is a vector, it has both magnitude and direction. We also know the equation F=ma to be true. Since a force is in a certain direction, it will only cause an acceleration in the direction of the force. The force in the x direction is 0 for ball 1, and the force in the y direction is unknown for ball 2, but it doesn’t matter because the force (or lack thereof) in the x direction has no effect on the motion of the balls in the y direction. The only force in the y direction is the gravitational force.

Now, the gravitational force is different between the two balls: the bigger force is applied to the bigger mass. However, the mass of a falling object does not affect the kinematic motion of that object as evident in the lack of mass in any kinematic equations. Both balls acceleration at 9.8 m/s^2 in the y direction and have the same initial velocity in the y direction of 0. Therefore, the balls will hit the ground at the same time.