Projectile Motion Vectors Part 2Vectors Part 2PVHS PhysicsPVHS Physics

Essential Questions

What is a vector? What is the difference between a scalar

and a vector? How do you add and subtract vectors? What are the horizontal and vertical

components of a vector? What is projectile motion? How can the motion of a projectile be

described by its horizontal and vertical vector components?

What we know…

A scalar has magnitude but no direction

A vector has magnitude and direction The resultant is a vector representing

the sum of two or more vectors Vectors can be added graphically

using the triangle or the parallelogram methods

Try this…

An A-10 normally flying at 80 km/hr encounters wind at a right angle to its forward motion (a crosswind). Will the plane be flying faster or slower than 80 km/hr?

60 km/hr

Crosswind

80 km/hr

Is the resultant greater than or less than 80 km/hr?

80 km/hr

60 km/hr

Add the vectors

Resultant

hr

km100

6080Resultant 22

Vectors

© 1996-2009 The Physics Classroom, All rights reserved.

2-D Coordinate System

In 2-D, a good reference is the x-y coordinate plane

X

Y

Remember… we can move a vector as long as we don’t change magnitude or direction

2-D Coordinate System

X

Y

Once you establish a coordinate system or frame of reference, you can begin to analyze vectors mathematically

First, resolve the vector into its x-component and its y-component

Determining Magnitude

The component vectors can represent the change in x and the change in y for the vector

To find the magnitude, d, of the vector, we use the Pythagorean Theorem:

X

Y

x

y

22

222

yxd

,or

yxd

d

Determining Direction

Once we have a frame of reference, the vector will make an angle, with the x-axis

We can use the tangent function to determine the value of

X

Y

x

yd

x

ytan

,orx

ytan

1

If using a calculator, be sure to set degrees or radians as appropriate

Try this…

While following directions on a map, a pirate walks 45.0m north then 7.5m east. What single distance and direction could he have walked to reach the treasure?

While following directions on a map, a pirate walks 45.0m north then 7.5m east. What single distance and direction could he have walked to reach the treasure?

o..

tan

m..d

58057

45

6455745

1

22

X

Y

45.0m

7.5m

d

Component Vectors

Just as we can add two vectors to create a resultant…

80 km/hr

60 km/hr

Resultant

Component Vectors

Any vector can be broken down into two vectors that are at right angles to one another These vectors are

called “component vectors”

The process of determining the components is called “Resolution”

Velocity

VerticalComponent

HorizontalComponent

Resolving Components

If we know the magnitude, d, and direction, we can also find the x and y components

X

Y

x

yd

cos

sin

,

cossin

dx

dy

ord

xand

d

y

Try this…

How fast must a truck travel to stay directly beneath and airplane that is moving 105 km/hr at an angle of 25 degrees to the ground?

X

Y

V=105 kph

Vtruck=?

hr/kmcos

cosvvtruck

9525105

Adding Vectors

Algebraically

Demo

Vector A=4.5m/s @ 35 degrees Vector B=6.5m/s @ -40 degrees Find A+B

Try this…

A ranger leaves his base camp for a ranger tower. He drives 35o south of east for 25.5 km and then drives 65o north of east for 41.0 km. What is the displacement from the base camp to the tower?

What we know…

What is a vector? What is the difference between a

scalar and a vector? How do you add and subtract

vectors? What are the horizontal and vertical

components of a vector?

http://www.physicsclassroom.com/Class/1DKin/U1L1c.html

Questions?