Unit 3-2: TrajectoriesUnit 3-2: Trajectories

Projectile MotionProjectile Motion

Projectile: Any object moving through the air that is only being affected by gravity Very similar to freefall The difference is that it also is moving side to

side.

A projectile moves through the air in a curved path called a trajectory.

Projectile: Any object moving through the air that is only being affected by gravity Very similar to freefall The difference is that it also is moving side to

side.

A projectile moves through the air in a curved path called a trajectory.

Projectile MotionProjectile Motion

Each projectile has a different trajectory based on its launch angle and starting velocity. Analyzing the trajectories by themselves can be

quite confusing, however we break them up into their components to make things easier.

Each trajectory has a horizontal and vertical component.

Each projectile has a different trajectory based on its launch angle and starting velocity. Analyzing the trajectories by themselves can be

quite confusing, however we break them up into their components to make things easier.

Each trajectory has a horizontal and vertical component.

Projectile MotionProjectile Motion

When the horizontal and vertical components are brought together, a parabolic trajectory is created.

Observe this next image, note how the distance between the horizontal movement never changes, because velocity is constant.

Observe how the vertical distance changes as time goes on, this is because gravity is accelerating the object.

When the horizontal and vertical components are brought together, a parabolic trajectory is created.

Observe this next image, note how the distance between the horizontal movement never changes, because velocity is constant.

Observe how the vertical distance changes as time goes on, this is because gravity is accelerating the object.

Projectile MotionProjectile Motion

QuickTime™ and a decompressor

are needed to see this picture.

Projectile MotionProjectile Motion

It is very important to remember that gravity only affects objects in the vertical component. Gravity has absolutely no effect on the

horizontal component.

It is very important to remember that gravity only affects objects in the vertical component. Gravity has absolutely no effect on the

horizontal component.

Avoiding the dreaded MATHAvoiding the dreaded MATH

This section will focus on determining the trajectory of a projectile graphically

It’s a lot faster and easier than any other method.

This section will focus on determining the trajectory of a projectile graphically

It’s a lot faster and easier than any other method.

How to draw a trajectoryHow to draw a trajectory

Start with a vector at an angle Draw the vector to scale on graph paper

Scale remains: 0.6cm = 10m/s = 1square

Now you determine your Vx. Remember that this remains constant.

Determine your Viy, this will decrease by 10m/s every second that goes by.

Start with a vector at an angle Draw the vector to scale on graph paper

Scale remains: 0.6cm = 10m/s = 1square

Now you determine your Vx. Remember that this remains constant.

Determine your Viy, this will decrease by 10m/s every second that goes by.

How to draw a trajectoryHow to draw a trajectory

Step 2: Draw, from the end of your first vector, Vx. Then, from where the Vx ended, draw in Viy,

but with one less square. This is because of gravity acting on it.

Draw in the resultant vector from beginning to end.

Step 2: Draw, from the end of your first vector, Vx. Then, from where the Vx ended, draw in Viy,

but with one less square. This is because of gravity acting on it.

Draw in the resultant vector from beginning to end.

How to draw a trajectoryHow to draw a trajectory

Step 3: Continue drawing Vx and then Vy until the

trajectory returns to the ground.

There are some rules for determining range, height and time, but we’ll discuss those shortly.

Ex: Draw the trajectory for 60m/s at 45°

Step 3: Continue drawing Vx and then Vy until the

trajectory returns to the ground.

There are some rules for determining range, height and time, but we’ll discuss those shortly.

Ex: Draw the trajectory for 60m/s at 45°

The RulesThe Rules

QuickTime™ and a decompressor

are needed to see this picture.

It says here:-To determine time, count all the resultant

vectors except the first.-To determine range, count all the Vx vector

squares except the first Vx vector. Each square represents 10m.

To determine height, count all the Vy vector squares except the first half of the Viy

vector

Let’s all try some examples!Let’s all try some examples!

QuickTime™ and a decompressor

are needed to see this picture.87m/s at 30°

102m/s at 18°87m/s at 76°