Tutorial Problems Week 9
November 28, 2012
The rotational kinematic equations:
=
=
=
2
=
0 + (t t0 )
1
0 + (0 + ) (t t0 )
2
1
2
0 + 0 (t t0 ) + (t t0 )
2
2
0 + 2 ( 0 )
Linear to angular relationships:
d = r
v
aT
= r
= r
where all angular quantities are in
Tutorial)Questions)for)Week)8)
)
1. A 2.0 m tall basketball player is standing a horizontal distance of 7.0 meters away from
a basketball hoop. The height of the hoop is 3.0 meters, and the basketball player throws
the ball at an angle of 60 degrees above
P2 Tutorial for Week 7
1. A 2.0 m tall basketball player is standing a horizontal distance of 7.0 meters away from
a basketball hoop. The height of the hoop is 3.0 meters, and the basketball player throws
the ball at an angle of 60 degrees above the horiz
Week 7
Motion in Two Dimensions
Read Sections 3.1 3.3
Clicker problem
A package is dropped by an airplane
traveling horizontally at 50 m/s at an
altitude of 1000m. What is the initial
velocity of package just after it leaves the
plane? As usual, ignore wi
Week 4 Tutorial Problems
Physics 2
Problem 1
Find the derivative of the following functions.
a) f (x) = 5 + 4x 5x2 + 7x5 b) g(x)
= esin(3x) +
line
Fall 2015
1
ln(x)
c)
h(x) = x2 sin(x)
Solution:
a) f (x) = 5 + 4x
0
5x2 + 7x5
d
d
d
+ 4 dx [x] 5 dx [x2 ] +
Week 8 Tutorial Problems
Physics 2
Problem 1
Evaluate the following indenite integrals:
R line
a) (Ax3
Bx2 + Cx + D)dx
R
Apply the power rule to each term xp dx =
R
R
R
R
A x3 dx B x2 dx + C xdx + D dx
= A x4 B x3 + C x2 + Dx + constant
4
3
2
b)
c)
Fall 2
Week 6 Tutorial Problems
Physics 2
Fall 2015
Problem 1
Calculate the dot product of the following pairs of vectors.
line
a) A = 4.0i - 6.0j, B = - 3.0j
~ ~
A B = (4
i
line
6 ( 3 =
j)
j)
12( + 18( =
i j)
j j)
12(0) + 18(1) = 18
b)A= 5 meters A = 30, B= 2 m
Problem 1
You are an Ottoman siege commander in charge of bombarding the city of Constantinople, which has
walls 50.0m high. Your cannons release their projectiles at an angle of 30.0 above the ground and at
100. m/s. Between what two distances from the c
Week 2 Tutorial Solutions
Physics 2
Fall 2015
line
Problem 1
a) First we need to convert 100 miles per hour to miles per second.
1 hr
min
100 miles 60min 1 60s = 1/36 miles
hr
s
Then apply the denition of average acceleration:
line
aavg,Drake = v = 1/36 m
Physics 2 Tutorial Problems Week 9
November 25, 2015
Part 1
1) A wheel with radius 2.0 m rotates such that its angular position as a
function of time is given by
= 10t + cos(t)
where is in radians and t is in seconds.
a) Derive an expression for the tang
Physics 2
Tutorial 3
1 , 201
Problem 1 Car Race. Recently, the exotic sports car company Bugatti released a new model of their
famed Veyron after an American car company developed a production sports car with a higher top speed
than the previous model of
Week 5 Tutorial Problems
Physics 2
Fall 2015
Give all answers to 2 signicant gures. All angles should be between 0 and 360o .
Problem 1
Convert the following vectors from Cartesian (x,y) to polar (r,) or polar to Cartesian coordinates.
a) (4, 6) (7.2, 300
Physics 2 Tutorial Week 1
September 30, 2015
1. Nyan the cat can meow at a rate of 20 meows in 5 seconds. If Nyan meows
for 3 minutes and 36 seconds, how many total meows will Nyan the cat have
performed during this time?
Solution:
(a) Find the rate R at
1. Calculate the rst derivative with respect to x of the following functions.
(a) f (x) = (x + )(x2 + x + )
Lets dene
g(x) = x + h(x) = x2 + x +
The problem can be written as
f (x) = g(x) h(x)
This is a classic product rule problem. Applying the product
Physics 2 Tutorial #6 Solutions, Fall 2012
1. Pierce decides to become a stunt motorcycle driver. For his rst jump, he
plans to ride o a ramp and be in free-fall until he lands on a second ramp that
is 5 meters lower than the rst. He will use ramps that m
Tutorial 5 Solutions
1) In your physics career, you will find it increasingly important to be able to
tailor your problem solving tactics to specific problems. One example of this
that you will often come across is the incline plane problem, in which a bl
Week 10 Tutorial Problems
(review for the nal exam)
Physics 2
Fall 2015
Problem 1
You have a very large supply of two solutions. Solution A is 10% ethanol by volume. Solution B
is 90% ethanol by volume. How much of each solution do you need to mix togethe
P2 Quiz1-Ques,on 1
You buy a 100 kg of Colby-Jack cheese at
Albertsons. The cheese is 45% Colby. In your
research, you have determined that the ideal
quesadilla is 30% Colby. How much Jack
cheese to you nee
Quiz Question 1-Week 5
!
Suppose velocity of object 1 is given by vector v1
which has magnitude 3 and direction +30 degrees,
and object 2 has velocity vector v2 with magnitude
3 and direction -30 degrees.
!
What is vector V, where V=v1-v2 ?
Draw 2 vectors
Physics 2 Week 5 Tutorial Vectors
1. In your physics career, you will find it increasingly important to be able to tailor your
problem solving tactics to specific problems. One example of this that you will often
come across is the incline plane problem,
Tutorial)Questions)for)Week)9)
)
1. Consider a Ferris wheel that is rotating at a rate of /4 radians per second in the
counterclockwise (CCW) direction when viewing it:
a) What is the Ferris wheels period of rotation?
b) What is the angular velocity in re
1. Pierce decides to become a stunt motorcycle driver. For his first jump, he plans to ride
off a ramp and be in free-fall until he lands on a second ramp that is 5 meters lower than
the first. He will use ramps that make angles of 25 to the ground. His m
P2 Week 6 Tutorial solutions: Relative Velocity
Note that this solution set uses the <i,j> notation for vectors. That is, for example,
v=<3,2>=3i+2j. Also, the _ means subscript, so V_k/L =Vk/L. We interp
Week 2 Tutorial Solutions
October 10, 2012
1. Florent Manaudou won the 50-meter freestyle at the London Olympics with a time of 21.34
seconds. The race was held in a pool that was 25m long, so the athletes start on one side, swim
the length of the pool, t
Quiz-Week10-Problem 1
Find the area under the curve described by
y(x)=(1/2)(x-x0) between x= -2 and x= 4.
Also, treat x0 as a constant.!
!
!
Quiz-Week10-Problem 2
The rate of painting a wall is described by the
function: dA/dt= 2 e-t/2 (essentially, the f
1. Calculate the first derivative with respect to x of the following functions.
(a) f (x) = (x + )(x2 + x + )
Lets define
g(x) = x + h(x) = x2 + x +
The problem can be written as
f (x) = g(x) h(x)
This is a classic product rule problem. Applying the prod
P2 Week 2 Solutions
We have kept extra digits into this solution to more closely match calculation. Generally, one more significant figure has
been added.
1. You toss a ball (mass 12 kg) straight vertically into the air. It takes 3s to come back to your h
P2 Quiz Week 8
2D mo/on- intermediate
intermediate 2D proj
An object is launched from the ground. At 2 seconds, the object is 40m
downrange and has a height of 35m. Assume +x is the direction that the
projectile travels, and +y is up.
1