CHAPTER FIVEProjectile Motion

QUICK REVIEW

What is the difference between scalar and vector quantities?

What are some examples of vector quantities? 75 mph east 65 N downward

Scalar quantities with direction don’t make sense (10 kg north, 5 liters east, etc)

VELOCITY VECTORS

We already know how to calculate the resultant of two vectors going in either the same or opposite directions, either add or subtract

OYB: An airplane traveling slowly north at 80km/h relative to the surrounding air encounters a tailwind of 20 km/h. What will be the resulting velocity? What would the resulting velocity be if it made a u-turn and flew into the wind?

VELOCITY VECTORS

Perpendicular vectors The resultant of two perpendicular vectors

is the diagonal of a rectangle constructed with the two vectors as sides.

3 5

4

VELOCITY VECTORS

Is there a special case for squares? Yes, the diagonal of a square is √2, times

the length of one of its sides

1 √2

1

OYB

Suppose that an airplane normally flying at 80 km/h encounters wind at a right angle to its forward motion—a crosswind. Will the airplane fly faster or slower than 80 km/h?

PHYSICS OF SPORT

Surfing– If you want to increase your speed, what do you do?

As you increase your angle relative to the wave front, the velocity also increases.

COMPONENTS OF VECTORS

Two vectors at right angles that add up to a given vector are known as the components.

Any vector can be “resolved” into two component vectors at right angles to each other.

The process of determining the components of a vector is called a resolution.

PROJECTILE MOTION

A projectile is any object that moves through the air or space, acted on by only gravity (and air resistance, if any) A stone thrown in the air, a cannonball

shot from the cannon, a spacecraft circling Earth

PROJECTILE MOTION

The horizontal component of motion for a projectile is just like the horizontal motion of a ball rolling freely along a level surface without friction. Without friction, a rolling ball moves at a

constant velocity. Ball would cover equal distances in equal

intervals

PROJECTILE MOTION

The vertical component of a projectile’s velocity is like the motion for a freely falling object. Gravity acts vertically downward A projectile accelerates downward with

increasing speed in the vertical direction covering a greater distance in each successive equal time interval

Or, if projected upward, the vertical distances of travel decrease with time on the way up

PROJECTILE MOTION

MOST IMPORTANT: horizontal component of motion for a projectile is independent of the vertical component of motion They are completely independent, their

combined effects produce the variety of curved paths the projectiles follow.

OYB: describe the components of projectile motion

PROJECTILES LAUNCHED HORIZONTALLY Which coin hit the ground first? Does your answer depend on the speed

of the coin? Explain The downward motion of a horizontally

launched projectile is the same as that of free fall.

A projectile’s path is called its trajectory.

PROJECTILES LAUNCHED AT AN ANGLE Remember, vertical distance is

independent of horizontal distance. With no gravity, a projectile would

follow a straight-line path. But because of gravity, it falls beneath the line the same vertical distance it would fall if released from rest.

What is the equation for distance in free fall?

d=1/2(g)(t)2

PROJECTILES LAUNCHED AT AN ANGLE If you toss a projectile skyward at some

angle, it isn’t moving at the speed at which you threw the object. Why?

The vertical distance a projectile falls below an imaginary straight-line path increases continually with time and is equal to 5t2 meters.

OYB

How long does the force of the thrower act on a ball tossed into the air?

A projectile is launched at an angle into the air. Neglecting air resistance, what is its vertical acceleration? What is its horizontal acceleration?

PROJECTILES LAUNCHED AT AN ANGLE Vertical range is affected by firing a

projectile at a steeper or lesser angle. Which would give a higher vertical range and which a lower?

Horizontal range is also affected by the angle at which the projectile is launched. Two different projection angles will have

the same horizontal range, two that add up to 90 degrees.

PROJECTILES LAUNCHED AT AN ANGLE The maximum range horizontally is

achieved at an angle of 45 degrees. Where would this information come in

handy? Batting, make contact at a 45 degree angle Throwing shot, discuss, or javelin

PROJECTILES LAUNCHED AT AN ANGLE Acceleration due to gravity is the same

coming up as going down, so speed it loses going up is the same speed it gains coming down. Therefore, the projectile hits the ground

with the same speed it originally had when it was projected upward from the ground.

OYB: Describe how far below an imaginary straight-line path a projectile falls

MY OWN “CHEESE STATEMENT”

Since the earth is curved, for long range projectiles we must account for the curvature. If an object were projected fast enough, it

will fall all the way around the Earth and become an Earth satellite.