Horizontal Acceleration Card - Unsolved Examples | PHYS 200, Quizzes of Physics

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Example 18:

A very curious student, 1.50 meters tall from feet to eye, stands

34.0 meters away from a tall flagpole. This student just happens to

have a triangulation sextant (a device for measuring angles from

the horizontal) and measures an angle of 22.5 degrees. How tall is

the flagpole?

Answer:

Example 19:

The same curious student, 1.50 m tall meters from feet to eye,

stands on the 10

th

street bridge and looks toward Duquesne

University. An angle of 15.0 degrees from the horizontal to the top

of the bluff is measured using a triangulation sextant. If this

student is standing 217 meters away from the bluff, how tall it?

Answer:

Scalar – a quantity that can be described by a single number

(and units)

Vector – a quantity described by a “strength” (its magnitude)

and a direction

Scalar Quantities Vector Quantities

Distance Displacement

Speed Velocity

Energy Force

Mass Acceleration

Temperature Electric Field

Having to keep track of a direction may seem to have little

consequence, but it can mean vector answers differ wildly

compared to scalar answers.

As a result, if you are required to supply an answer that is a vector

you must include a magnitude and direction. For the direction to

make sense, it is very helpful to include a coordinate axis. Your

choice of a coordinate axis will be required for quiz and exam

problems dealing with vector quantities.

If a problem dealing with a vector quantity asks for just the

magnitude of the vector, only a positive number with appropriate

units is required. Giving a direction in this case is wrong.

Similarly, if you are working with a scalar quantity and you give a

direction in your answer, you are giving an incorrect answer.

Vector Addition & Subtraction – An Introduction

When dealing with vector addition and subtraction using algebra it

is helpful to introduce some concepts.

Vector components:

In this class we will work with two dimensions most of the time.

Using a standard coordinate axis, these dimensions are referred to

as the x and y dimensions. A two dimensional vector (magnitude

and direction) can be decomposed into its vector components.

These vector components are found using trigonometric functions

and describe how much of the vector lies in each dimension.

Notation of Vector Components:

Algebraically, a decomposed vector will be written in the

following form (called component form)

€

A = A

x

x + A

y

y

Here, A

x

and A

y

are the magnitudes of the vector components.

€

x and

€

y tell you in which direction these magnitudes point.

Examples:

Vector Addition & Subtraction – Algebraic Method

Method:

1. Take every vector written in magnitude-direction form and “break”

each vector into its components (x and y). Do this in an organized

manner to avoid confusion.

2. Write each vector in terms of its components using

€

ˆ x and

€

ˆ y notation.

This is called the “component form” of the vector.

3. Add like components. For vector subtraction, add the negative of the

components you got from step 2.

4. Find the resulting vector’s magnitude using the Pythagorean theorem.
5. Find the resulting vector’s direction from the definition of the tangent

function. Be very careful here, the tangent function is restricted to

angles between 0˚ and 90˚ on most calculators. You must be aware

your calculator’s angle may only be a “reference angle”.

Pros – much quicker than the graphical method

Cons – not very visual

Example 20: Vector

€

A has a magnitude of 5 km and is oriented

30˚ from the horizontal. Write vector

€

A in component form.

Example 21: Vector

€

B has a magnitude of 6 m/s and is oriented

40˚ from the vertical. Write vector

€

B in component form.

Example 22: Vector

€

C has a magnitude of 7 km and is oriented

135˚ from the horizontal. Write vector

€

C in component form.

Example 23: Vector

€

D has a magnitude of 8 m/s and is oriented

240˚ from the positive y-axis. Write vector

€

D in component form.