* ANSWERS!! (not complete)* TEST 1 Q2 PHYSICS

CHAPTER
3 Relative Motion, Vectors,
2-dimensional (projectile) motion

Relative
motion:

Explain the
concepts of

Reference
frames

* The idea of point of view, constant
speed.*

Relative
velocity

* Velocities measured relative to another
object’s reference frame..*

Special
relativity

*The
idea that light is NOT relative, so then objects moving close to the speed of
light slow down (time dilation) and shrink (length contraction). *

Sketch
the path of a ball thrown on a moving train from the point of view of the
train, the ball, an observer on the ground, an observer on another train… both
for a normal train and one moving close to the speed of light.

*Train…
ball goes up and down, ball… all is still, observer on ground.. parabola!,
other train.. some type of parabola… width depends on the difference in
speeds…. For moving close to the speed of light, parabolas are narrower.*

How
to find the velocity of one object with respect to another if you know the
velocity of each with respect to the ground…

*V12=V1g-V2g*

* *

Vectors:

Relative
motion with 2 dimensions instead of one.

*Add
vectors*

What
is a vector?

*Property
that has a number, unit, and direction….. arrow, length of arrow is the
magnitude.*

How
to add vectors to find the resultant (head to tail: graphical method, right
triangles… (law of sines??) ).

*Graphical
method, add head to tail, draw a resultant arrow vector from start to finish
and complete the triangle. Measure length and direction angle.*

*With
right triangle… change each vector hypotenuse into x and y components, using
x=Hcos(angle), y = H sin (angle). Add all the x’s and y’s, make one big right
triangle and solve for new hypotenuse using pythogorean theorem and inverse
tangent for angle*

What
properties are vectors?

*Things
like displacement, velocity, acceleration, force, weight. *And which are scalars?*
Things like distance, speed, mass, energy.*

How
and why there are 6 ways to add three vectors.

*Draw
head to tail: A+B+C, A+C+B, B+C+A, B+A+C, C+A+B, C+B+A*

How
to find the angle of the resultant.* Measure, or do inverse tangent of big
right triangle…*

How
to find the x/y, horizontal/vertical, north/east, components of a vector at an
angle.

*With
right triangle… change each vector hypotenuse into x and y components, using
x=H cos(angle), y = H sin (angle). Add all the x’s and y’s, make one big right
triangle and solve for new hypotenuse using pythogorean theorem and inverse
tangent for angle*

Projectile
motion:

Why
and how do we separate motion into x/y perpendicular components?* Well,
because it makes the math easier (right triangles), because forces that are
perpendicular do not affect each other, and because gravity only acts in one
direction.*

What
is projectile motion?

*An
object moving through the air (with no air resistance),starting with some
velocity at an angle, with no
force acting on it except for gravity.*

What
is the path of a projectile and how does this explain why you CAN’T make a
vector of displacements in projectile motion? *A parabola !*

What
property is the same in the x and y direction for projectile motion?

*Time!!!*

What
is the angle of maximum range for a projectile and why?

*45
degrees because the same component of velocity in the y as in the x.*

What
information do you know about a projectile while it is at the top of its arc?

*Its
velocity in the y is zero.(Ay is – 9.8, Vx=Vx, time is half of the total
time of the trip)*

What
information do you know about a projectile fired horizontally?

*Its
velocity in the y starts at zero.(but Vx = Vx, Ay =-9.8, etc..)*

What
information do you know about a projectile fired from the ground that lands on
the ground?

*Its
starting velocity Vx=Vx, and Viy=Vfy, and the Dy = 0, (Ay=-9.8, etc..)*

Draw
a strobe diagram of the vertical and horizontal components of a projectile’s
motion.

*.
. . . . . . . . . . . . . . . . . . . . . . (horizontal is constant)*

* *

*vertical
is accelerated:*

*.
. . .
. . . . .*

What
formula is always used in the x direction and why?

*Since
Ax=0, Dx=VxT is all you need…*

*Vx
= V cos (angle)*

What
formulas are usually used in the y direction?

*Viy=V
cos (angle)*

*And*

*Dy=ViyT+1/2AyT ^{2}*

*Vfy=Viy
+ AyT*

*Vfy ^{2}=Viy^{2}+
2AyDy*

*Ay
= -9.8 m/s ^{s}*

----------------------------------------------------------------

Why can you never answer “how fast are you going”?

*You always are moving different relative to
something else…there is no one true fram of reference, you are the center of
your universe!*

A passenger on a train going east is skateboarding
towards the back, while throwing a spear towards the front, while there is an
ant walking towards the point of the spear.

Describe the path of the spear as seen from the:
passenger, ground, ant, train.

How would you calculate the velocity of the ant?

A piece of chalk is dropped by a teacher
walking at a speed of 1.5 m/s. From the teacher's perspective how does the
chalk appears to fall? How does it fall from the ground’s point of view?

*Down, parabola*

Why are there two answers to the
question: How far did you travel?

*Distance travelled, displacement*

Two vectors acting at right angles to
each other having the magnitude 6 and 8 have a resultant with a magnitude of

*10 (Pythagoreas)*

What are quantities that are given as scalar or vectors? *Things like displacement,
velocity, acceleration, force, weight. *And which are scalars?* Things like distance,
speed, mass, energy.*

* *

What does a vector mean?

*Property that has a number, unit, and
direction….. arrow, length of arrow is the magnitude.*

How would parabolic motion be different at speeds
close to the speed of light?

*….
For moving close to the speed of light, parabolas are narrower.*

Describe the two ideas (postulates) that lead
to the theory of special relativity:

*All frames of reference equal, you are the
center of your universe, speed of light is constant for all observers, not
relative, nothing goes above c!*

What are the consequences of special
relativity? (How do the properties we know change at speeds close to the speed
of light?)

*Time dilates, length contracts*

A small airplane flies at a velocity of
145 km/h toward the south as observed by a person on the ground. The airplane
pilot measures an air velocity of 170.0 km/h south. What is the velocity of the
wind that affects the plane?

*Vpg= 145, Vpw=170m Vwg=??*

*Vpg=Vpw+Vwg, so Vwg=145-170=-25 south or 25 km/hr
North=Wind*

While following directions on a treasure map, a
person walks 75.0 m south, then turns and walks 4.50 m east. Which single
straight‑line displacement could the
treasure hunter have walked to reach the same spot?

*75.13 m at 86.6° S of E*

A boat crosses a 30 meter wide river with an
initial speed of 20 m/s aimed straight across (perpendicular to the current).
If the current is 5 m/s, where and when will the boat reach the other side?

*1.5 sec later, 30.9 m at an angle of
75.96° to the bank, or 7.5 m downstream.*

* *

If a plane is pointed due east, but the path
it takes from the ground is due south, the wind must be blowing

*SW*

If I take a journey and walk three different
legs to my journey, describe how to calculate the total displacement.

*Graphical
method, draw head to tail,: A+B+C, A+C+B, B+C+A, B+A+C, C+A+B, C+B+A draw a
resultant arrow vector from start to finish and complete the triangle. Measure
length and direction angle.*

* *

*Or
With right triangle… change each vector hypotenuse into x and y components,
using x=H cos(angle), y = H sin (angle). Add all the x’s and y’s, make one big
right triangle and solve for new hypotenuse using pythogorean theorem and
inverse tangent for angle*

What are the conditions necessary for projectile
motion? Describe the change in vertical and horizontal velocity

What does a strobe diagram seen from above
(projected horizontally) look like for an object that is thrown in the air?

What does a strobe diagram seen from head on
(projected vertically) look like for an object that is thrown in the air?

An arrow is shot in the air with a
velocity of 61 meters per second at an angle of 20 degrees. How high will the
arrow go?

*22.2 m*

A stone is thrown at an angle of 30.0° above
the horizontal from the top edge of a cliff with an initial speed of 12 m/s. A
stopwatch measures the stone's trajectory time from the top of the cliff to the
bottom at 5.6 s. What is the height of the cliff?

*120.1 m*

A model rocket flies horizontally off the
edge of the cliff at a velocity of 50.0 m/s. If the canyon below is 100.0 m
deep, how far from the edge of the cliff does the model rocket land?

*225.9 m*

Where would a baseball pitcher have to
aim a fastball to have it pass at the height of a batter's chest? Why?

*Above*

* *

In projectile motion, the rising and
falling times are equal if the landing position is related how to the launching
position?

*=*

A firefighter 60 meter away from a
burning building directs a stream of water from a fire hose at an angle of 30
degrees above the horizontal. If the velocity of the stream is 20 m/s, at what
height will the stream of water strike the building?(on earth with no air
resistance)

*10.48m*

** Honors: at what angle should you hold
the hose in order to hit the building level with you?

*No answer! Max range is 40.8 m*

** Honors: Calculate the journey of a
man who walks 50 miles at 76 degrees west of south, then 40 miles at 65 degrees
north of east for 3 hours in each leg. What is the velocity of a plane that
wants to catch him exactly, that is being blown by a 12 mph north wind?

*39.7833 miles away at 37.3869‘ n of w*

* *

*plane aim 9.56 mph at 56 ‘ s of w *