## 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?

Ball 2 because it has greater mass than ball 1

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

#### 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. 