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SPH3U

Projectile Motion

Projectile Motion is motion with a _________________ ___________________

____________________ combined with a _________________

_________________ ___________________________ caused by gravity.

A projectile is an object that moves through the air, along a __________________

without a ___________________________ system.

What forces are acting on the projectile once it leaves the gun? Answer: __________________________!

Date: __________________

The horizontal component of a projectile velocity is ________________________

The projectile experiences constant downward acceleration due to gravity

Notice that if you subtract v⃗1from v⃗2 to find Δ v⃗ the resultant vector goes straight down. This is the direction of the acceleration, which is how we can be assured the acceleration is straight down towards the earth. It is caused entirely by gravity.

The horizontal and vertical motion of a projectile are independent of each other, except they have a common time.

This of course is based on the assumption that air resistance can be ignored.

Projectiles basically move in two directions __________________________ ( the x

direction) and ______________________________ (the y direction).

When analyzing the motion of a projectile, we consider each case separately.

Horizontal Motion

The horizontal displacement of a projectile is called the __________________________.

There is only one equation used for horizontal motion of a projectile.

Vertical Motion

Vertical motion happens in the y-direction. There are several useful equations we can consider for this motion:

Example 1: A stone is thrown horizontally with an initial speed of 8.0 m/s from a cliff. Air resistance is negligible. (a) Determine the horizontal range of the stone after 2 seconds.(b) Determine the vertical displacement of the stone after 2 seconds.(c) Determine the instantaneous vertical velocity of the stone after 3 seconds.

More Notes on Projectiles

We have already done problems where the projectile was fired horizontally:

But, what do you do if the projectile is not shot horizontally? For example, if the initial velocity is at an angle?

** Things become more complex when a projectile is shot at some angle instead of straight across. We have to take the initial velocity and break it up into a horizontal and vertical component in order to analyze the motion.

Example 2 A golf ball is hit with an initial velocity of 70m/s [50 up from the horizontal]. Find vix (the initial velocity in the x direction) and viy (the initial velocity in the y direction).

Example 3

A cannon is set at an angle of 45 above the horizontal. A cannonball leaves the muzzle with a speed of 220 m/s. Air resistance is negligible. Determine the cannonball’s:

a) maximum heightb) time of flightc) horizontal range (assuming the ground is level)d) velocity at impact.

SPH3U

Projectile Motion

Projectile Motion is motion with a constant horizontal velocity

combined with a constant vertical acceleration caused by gravity.

A projectile is an object that moves through the air, along a trajectory

without a propulsion system.

What forces are acting on the projectile once it leaves the gun? Answer: Only Gravity!

Date: __________________

The horizontal component of a projectile velocity is constant

The projectile experiences constant downward acceleration due to gravity

Notice that if you subtract v⃗1

from v⃗2 to find Δ v⃗ the resultant vector goes straight down. This is the direction of the acceleration, which is how we can be assured the acceleration is straight down towards the earth. It is caused entirely by gravity.

The horizontal and vertical motion of a projectile are independent of each other, except they have a common time.

This of course is based on the assumption that air resistance can be ignored.

Projectiles basically move in two directions Horizontally ( the x direction) and Vertically (the y direction).

When analyzing the motion of a projectile, we consider each case separately.

Horizontal Motion

The horizontal displacement of a projectile is called the horizontal range (Δx)There is only one equation used for horizontal motion of a projectile.

initial velocity=horizontal rangechange∈time

Vertical Motion

Vertical motion happens in the y-direction. There are several useful equations we can consider for this motion:

Example 1

A stone is thrown horizontally with an initial speed of 8.0 m/s from a cliff. Air resistance is negligible. (a) Determine the horizontal range of the stone after 2 seconds.(b) Determine the vertical displacement of the stone after 2 seconds.(c) Determine the instantaneous vertical velocity of the stone after 3 seconds.

SPH3U

More Notes on Projectiles

Yesterday we did problems where the projectile was fired horizontally:

But, what do you do if the projectile is not shot horizontally? For example, if the initial velocity is at an angle?

** Things become more complex when a projectile is shot at some angle instead of straight across. We have to take the initial velocity and break it up into a horizontal and vertical component in order to analyze the motion.

Ex. 1. A golf ball is hit with an initial velocity of 70m/s [50 up from the horizontal]. Find vix (the initial velocity in the x direction) and viy (the initial velocity in the y direction).

Date: __________________

Example 3

A cannon is set at an angle of 45 above the horizontal. A cannonball leaves the muzzle with a speed of 220 m/s. Air resistance is negligible. Determine the cannonball’s:

a) maximum heightb) time of flightc) horizontal range (assuming the ground is level)d) velocity at impact.