Ch 3 – Ch 3 – Two-Dimensional Motion Two-Dimensional Motion

and Vectorsand Vectors

Scalars vs. VectorsScalars vs. Vectors

►Scalar – a measurement that has a Scalar – a measurement that has a magnitude (value or number) onlymagnitude (value or number) only Ex: # of students, age, speed, distanceEx: # of students, age, speed, distance

►Vector – a measurement that has both Vector – a measurement that has both a magnitude a magnitude andand a direction a direction Ex: displacement, acceleration, velocityEx: displacement, acceleration, velocity

Vectors and directionVectors and direction

Vectors can be added Vectors can be added graphicallygraphically

►Animation

►Resultant: a vector representing the Resultant: a vector representing the sum of two or more vectorssum of two or more vectors

Vectors at right angles can be Vectors at right angles can be added using the Pythagorean added using the Pythagorean

theoremtheorem► AA22 + B + B22 = C = C22

► The angle can be found The angle can be found using SOH CAH TOAusing SOH CAH TOA

► SOH: Sin SOH: Sin θθ = opp/hyp = opp/hyp► CAH: Cos CAH: Cos θθ = adj/hyp = adj/hyp► TOA: Tan TOA: Tan θθ = opp/adj = opp/adj► If you are looking for If you are looking for θθ::

ΘΘ = Sin = Sin-1-1(opp/hyp)(opp/hyp) ΘΘ = Cos = Cos-1-1(adj/hyp)(adj/hyp) ΘΘ = Tan = Tan-1-1(opp/adj)(opp/adj)

©2008 by W.H. Freeman and

Company

Let’s practiceLet’s practice

►Find the component velocities of a Find the component velocities of a helicopter traveling 95 km/h at an helicopter traveling 95 km/h at an angle of 35angle of 35°° to the ground. to the ground.

►Vy = 54 km/hVy = 54 km/h►Vx = 78 km/hVx = 78 km/h

3-4: Relative Motion3-4: Relative Motion

If a boat is traveling north at 5 m/s and the current is east at 2 m/s, what is the relative

velocity of the boat to the shore?

3-33-3

►Two balls dropped

If there was no gravity…If there was no gravity…

With gravityWith gravity

What is a projectile?What is a projectile?►A A projectileprojectile is any object is any object

that falls through the air. that falls through the air. These objects are These objects are accelerated downward by accelerated downward by the force of gravity. the force of gravity.

►The KEY is that the ONLY The KEY is that the ONLY FORCE acting on the FORCE acting on the projectile is GRAVITY!projectile is GRAVITY!

I don’t want to

be a projectil

e!

Since gravity only acts in the vertical direction, then motion in the horizontal direction is constant!!

We will use 2 main formulas to solve these problems: 21

2

x

y gt

x v t

v

vx

vy

vy = v sin vx = v cos

Important concepts are: horizontal velocity component is always constantThere is no acceleration in the horizontal direction.

co n sta n t h o rizo n ta l ve loc ityvx

ve rtica l ve loc ity in c rea se s w ith tim e vy

vx

A ball is rolled off a table with a horizontal velocity of 2 m/s. If the table is 1 m tall, how long with it take the ball to hit the ground?

How far away from the bottom of the table will the ball land?