Ch 3 – Two-Dimensional Motion and Vectors

Scalars vs. Vectors ► Scalar – a measurement that has a magnitude (value or number) only  Ex: # of students, age, speed, distance ► Vector – a measurement that has both a magnitude and a direction  Ex: displacement, acceleration, velocity

Vectors and direction

Vectors can be added graphically ► Animation Animation ► Resultant: a vector representing the sum of two or more vectors

Vectors at right angles can be added using the Pythagorean theorem ► A 2 + B 2 = C 2 ► The angle can be found using SOH CAH TOA ► SOH: Sin θ = opp/hyp ► CAH: Cos θ = adj/hyp ► TOA: Tan θ = opp/adj ► If you are looking for θ:  Θ = Sin -1 (opp/hyp)  Θ = Cos -1 (adj/hyp)  Θ = Tan -1 (opp/adj)

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Let’s practice ► Find the component velocities of a helicopter traveling 95 km/h at an angle of 35° to the ground. ► Vy = 54 km/h ► Vx = 78 km/h

3-4: 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?

3-3

► Two balls dropped Two balls dropped Two balls dropped

If there was no gravity…

With gravity

What is a projectile? ► A projectile is any object that falls through the air. These objects are accelerated downward by the force of gravity. ► The KEY is that the ONLY FORCE acting on the projectile is GRAVITY! I don’t want to be a projectile!

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:

v y = v sin  v x = v cos  Important concepts are:  horizontal velocity component is always constant  There is no acceleration in the horizontal direction.

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?