### Lectures 7, 8, 9

```Physics 218: Mechanics
Instructor: Dr. Tatiana Erukhimova
Lectures 7, 8, 9
Overview of Today’s Class
•Hw Quiz
•Vectors
You want to measure
the height of a
building. You stand
2m away from a 3m
pole and see that it’s
“in line” with the top
of the building. You
measure 16 m from
the pole to the
building.
What is the height of
the building?
16 m
1. Draw a diagram
2. Choose x and y axes. Choose them in a way that make
your work easier. (E.g. choose one axis along the
direction of one of the vectors so that the vector will
have only one component).
3. Resolve each vector in x and y components
4. Calculate each component using sine and cosine. Be
careful with signs: any component that points along the
negative x or y axis gets a negative sign.
5. Add the x components together to get the x component
of the resultant. Similar for y:
Vx=V1x+V2x+…
Vy=V1y+V2y+…
6. If you want to know the magnitude and direction of
the resultant vector,
V  V V
2
x
2
y
tan 
Vy
Vx
CRAYFISH, SWAN, AND PIKE
(Translation of I. Krylov's fable)
Let crayfish, swan and pike
Each being just a part
Of harness they dislike.
They try a lot, and everyone
Starts pulling it with zeal;
The problem is that each of them
With his path wants to deal!
The swan makes upward for a cloud,
The crayfish falls behind;
The pike dives sharply in the deep,
And cart moves not from site.
The moral of the verse is that
Accordance should prevail
Amid the people who have plans
To work but not in vain.
Russian fable: Swan, Crawfish, and Pike
Fs
Lake

Despite
their
huge effort the
box does not
move!

River
Fp
Fc
Find Fs and Fc if Fp, θ, and  are
given
Quiz

 
and b  7i  3 j :
  
a) Find the components of the vector r  a  b



Given two vectors, a  4i  6 j
b) Find the magnitude of
makes with the x axis.

r
and the tangent of the

angle r
Given two vectors,

  
 
A  4i  3 j and B  5i  2 j
a) find the magnitude of each vector
b) Write an expression for the vector difference
 
A  B using unit vectors
 

a) Express the vectors F1, F2, and F in terms of their components.
3
y

F2
2
3

F3
x
1

F1

F4 ,
b) Find the components of the fourth force,
that should be
added for the object to be in static equilibrium.
A cannon at the origin points up at an angle θ with
the x axis. A shell is fired which leaves the barrel
with a velocity of magnitude Vm.
a) When does the shell reach its maximum height?
b)What is the maximum height?
c) What is the range (horizontal distance)?
d)What is the velocity of the shell when it hits the
ground?
A can drops from a magnet just when a bullet is shot from a
gun: Find the angle that the gun must be aimed at to hit the
can.
y
vi
H
θ
D
x
A physics professor did daredevil stunts in his spare
time. His last stunt was an attempt to jump across a
river on a motorcycle. The takeoff ramp was inclined
at 53.00, the river was 40.0 m wide, and the far bank
was 15.0 m lower than the top of the ramp. The river
itself was 100 m below the ramp. You can ignore air
resistance. a) What should his speed have been at the
top of the ramp to have just made it to the edge of the
far bank? b) If his speed was only half the value
found in (a), where did he land?
A faulty model rocket moves in the xy-plane (the positive ydirection is vertically upward). The rocket’s acceleration has
components ax(t)=t2 and ay(t)=-t, where =2.50 m/s4, =9.00
m/s2, and =1.40 m/s3. At
 t=0 the rocket is at the origin and has

velocity v0  v0 x i  v0 y j with v0x  1.00 m / s and v0 y  7.00 m / s.
a) Calculate the velocity and position vectors as functions of time.
b) What is the maximum height reached by the rocket?
c) What is the horizontal displacement of the rocket when it
returns to y=0?
Have a great day!