Презентация - Projectile motion

PROJECTILE MOTION

Essential question
How do the horizontal and vertical components of a projectile's velocity change as it moves through its path?

Projectile motion is a two dimensional motion under the influence of gravity. This makes projectile motion a special kind of free fall.

Since projectile motion is a special kind of free fall, mass does not affect the rate of fall.

Projectile motion has horizontal and vertical components and these 2 components are independent of each other.

Trajectory is the path travelled by a projectile and is parabolic.

Range is the horizontal distance that a projectile traverses from the point where it is launched to the point it lands.

Two Types of Projectile Motion

HORIZONTALLY LAUNCHED A projectile is launched or thrown completely horizontally Examples: a rock thrown horizontally off a cliff There is no upward trajectory

YESTERDAY’S ACTIVITIES… Activities 2 & 3 Marbles, wooden and steel balls rolling off

Marble 1 was dropped; Marble 2 was given a horizontal push

NON – HORIZONTALLY LAUNCHED Launched at an angle. The initial velocity of the projectile can be broken into horizontal (vix) and vertical velocities (viy).

YESTERDAY’S ACTIVITIES… Activity 1 Yellow stress ball was thrown underhand and was caught by your group mate

The horizontal velocity of a projectile is constant. Any projectile has zero horizontal acceleration.

For non – horizontally launched projectiles, the velocity decreases as they go higher and then increases as they go down.

The velocity of a projectile at its peak is zero.

The vertical velocity of a projectile is changing at a constant rate. The vertical acceleration of any projectile is

Qualitative analysis of projectile motion in the y-axis
Earth exerts a gravitational force on a projectile, so its upward speed decreases until it stops at the highest point, and then its downward speed increases.

Qualitative analysis of projectile motion in the x-axis
No object exerts a horizontal force on a projectile. Thus, according to Newton's first law, the ball's horizontal velocity does not change once it is released.

The vertical component at the maximum height is ZERO!
It will have the exact same velocity as it was launched with!

Vertical velocity is the same at the same height.
+2 m/s
-2 m/s

Qualitative analysis of projectile motion
Time it takes to reach the ground (horizontal push)
Time it takes to reach the ground (dropped)
=

Qualitative analysis of projectile motion

projectile launched at an angle

Quantitative analysis of projectile motion: Velocity
For a projectile launched at speed v0 at an angle θ relative to the horizontal:

SAMPLE PROBLEM
A football is kicked at an initial velocity of 20.0 m/s at an angle of 37.0o from the horizontal. Find the football’s time of flight, maximum height and range.

Example 3.9: Shot from a cannon
Stephanie Smith Havens is to be shot from an 8-m-long cannon at 100 km/h. The barrel of the cannon is oriented 45° above the horizontal. She hopes to be launched so that she lands on a net that is 40 m from the end of the cannon barrel and at the same elevation (our assumption). Estimate the speed with which she needs to leave the cannon to make it to the net.

Quantitative analysis of projectile motion: Using our kinematics equations
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