College Physics I – Recitation Week 13 Name _________________________________ Section ______

Review problems
The final exam is comprehensive, so this week, you will work on some practice problems form previous chapters so
that you remind yourself of these concepts before having to review for the final exam.
Important note: This review is only for problems from each major topic we have discussed. It obviously does not
include everything you would need to know on a final exam from prior topics because there is so much that it would
be impossible to condense it down to a few problems that can be done in a one-hour recitation. It also doesn’t cover
all the different types of problems you could potentially see on the final exam from these topics.
I. 1D kinematics
Equations 1D general: Equations 1D free fall:
1
𝑥𝑓 = 𝑥𝑖 + 𝑣𝑖 𝑡 + 2 𝑎𝑡 2 𝑦𝑓 = 𝑦𝑖 + 𝑣𝑖 𝑡 − 4.9 𝑡 2
𝑣𝑓 = 𝑣𝑖 + 𝑎𝑡 𝑣𝑓 = 𝑣𝑖 − 9.8 𝑡
𝑣𝑓 2 = 𝑣𝑖 2 + 2𝑎 (𝑥𝑓 − 𝑥𝑖 ) 𝑣𝑓 2 = 𝑣𝑖 2 − 19.6 (𝑦𝑓 − 𝑦𝑖 )
Important comments about problem solving:
 The equations connect an initial with a final situation. Whenever you use these equations for ANY
question, you need to think explicitly about what is the initial and what is the final situation. Do this in
Step 1.
o Draw both the initial and final situations.
o Use your drawings to determine 𝑥𝑖 , 𝑥𝑓 , 𝑣𝑖 , 𝑣𝑓 , 𝑎, and 𝑡. If you don’t know any of these, just
write e.g., 𝑣𝑓 =?
o Once you write down all these, it will be pretty obvious which equation you should use. This
makes solving the problem much easier!
 It’s a good idea to draw both the initial and final situations; visual information is easier to process by our
brains, and this helps you have a good understanding of what the problem is about.

For both problems on the next page, use this problem solving strategy!

Created by Alexandru Maries 13-1

Review problems
A. A grazing antelope first notices a lion attacking when the lion is 10.0 m away and moving toward the antelope at
a speed of 7.0 m/s. The antelope begins to accelerate away from the lion at 2.0 m/s2. Does the lion catch the
antelope? If no, explain why not, if yes, how much time does it take and how much distance does the lion run
before catching up with the antelope?

B. A hot-air balloon is traveling vertically upward at a constant speed of 5.0 m/s. When the balloon is 21 m
above ground, a package is released from the balloon which eventually hits the ground directly below the
balloon. Calculate the following:
a. The time the package spends in the air.
b. The speed of the package right before it hits the ground.
c. The height of the balloon at the moment the package hits the ground.

 Compare your answers to your group before proceeding. Consult with your TA if consensus cannot be reached.

Created by Alexandru Maries 13-2

Review problems
II. Projectile motion
Equations:
𝑥𝑓 = 𝑥𝑖 + 𝑣𝑖𝑥 𝑡 𝑣𝑖 𝑣𝑖𝑥 = 𝑣𝑖 cos 𝜃
𝑦𝑓 = 𝑦𝑖 + 𝑣𝑖𝑦 𝑡 − 4.9 𝑡 2
𝑣𝑓𝑦 = 𝑣𝑖𝑦 − 9.8 𝑡
𝜃 𝑣𝑖𝑦 = 𝑣𝑖 sin 𝜃
𝑣𝑓𝑦 2 = 𝑣𝑖𝑦 2 − 19.6 (𝑦𝑓 − 𝑦𝑖 )
Important comments about problem solving:
 The equations connect an initial with a final situation. Whenever you use these equations for ANY
question, you need to think explicitly about what is the initial and what is the final situation. Do this in
Step 1.
o Draw both the initial and final situations.
o Use your drawings to determine 𝑥𝑖 , 𝑥𝑓 , 𝑦𝑖 , 𝑦𝑓 , 𝑣𝑖𝑥 , 𝑣𝑓𝑥 , 𝑣𝑖𝑦 , 𝑣𝑓𝑦 and 𝑡. If you don’t know
any of these, just write e.g., 𝑣𝑓𝑦 =?
o Once you write down all these, it will be pretty obvious which equation you should use. This
makes solving the problem much easier!
 It’s really important to draw both the initial and final situations; visual information is easier to process by
our brains, and this helps you have a good understanding of what the problem is about.
 The equations have 𝑣𝑖𝑥 , 𝑣𝑖𝑦 , and NOT 𝑣𝑖 . So make sure you NEVER use 𝑣𝑖 when plugging in things
into a projectile motion equation!
For both problems on the next two pages, use this problem solving strategy!

Created by Alexandru Maries 13-3

Review problems
A. Two cats (Fuzz Aldrin and Ramses) are startled by something and jump from a height of 2.5 m at the same
speed of 2.5 m/s. Fuzz Aldrin jumps 45° above the horizontal and Ramses jumps 45° below the horizontal.
Calculate the following:
a. Fuzz Aldrin’s max height.
b. Ramses’ speed when he hits the ground.
c. How much more time Fuzz Aldrin spent in the air compared to Ramses.

Created by Alexandru Maries 13-4

Review problems
B. Dennis, a senior in high school, is preparing for the greatest food fight prank of all time. He plans to launch
watermelons from his homemade melon cannon machine towards the enemy food fighters standing on the
rooftop lunch area. The enemies are 10 meters from the edge of the 7-meter-high balcony. Dennis plans to
hide in some bushes away from the building to fire his cannon. The cannon fires at 22.0 m/s & must be angled
40° above ground to clear the bushes.
a. How far from the base of the building should Dennis place the cannon?
b. The teachers’ lounge window is 14 above the ground. Will they be able to see the watermelons pass by
their window (assume they are looking horizontally?

 Compare your answers to your group before proceeding. Consult with your TA if consensus cannot be reached.
Created by Alexandru Maries 13-5
Review problems
III. Newton’s 2nd law
Equations:
 On problem solving strategy shown below
 𝑓𝑠,max = 𝜇𝑠 𝐹𝑁 → ONLY use this equation if you have static friction, AND there is something in the problem
that implies the force of static friction is maximum. For example, if things are just about to start sliding.

Important comments about problem solving:

 By far, the most important thing is to get the correct FBD. If you don’t get that right, what you do next
doesn’t matter because you will get the problem wrong since you have the wrong FBD.
 Always double check your FBD and make sure it’s right before moving on. You should spend significant time
on it, it’s the most important step!
 The xy coordinate system is determined by the direction of acceleration. Either the x or the y direction will be
in the same direction as the acceleration (usually it’s the x direction that is chosen to be the same as the
direction of acceleration).
o If there is no acceleration, you can use any coordinate system, so use the one that is most convenient (has
the least number of forces that need to be broken up).
o For circular motion, there is always an acceleration towards the center of the circle equal to 𝑣 2 /𝑅. So one
coordinate direction will always be towards the center of the circle.
 In Step 3, don’t forget to visually break up the forces that are not along x or y, and give those components
names
o For example: Nx or Ny
o It often helps to write the components in terms of N and 𝜃. So instead of writing Nx or Ny, you can write
𝑁 sin 𝜃, 𝑁 cos 𝜃 on your FBD.
 In Step 4, we always write the equation by doing larger force minus smaller force. So it helps to always think
about this before you write the equations (“which force is larger?”)

For both problems on the next two page, use this problem solving strategy!

Created by Alexandru Maries 13-6

Review problems
A. Three blocks are connected with a rope so that one hangs
over the edge of the table as shown in the figure. They are
released from rest. Assume the table and pulley are
frictionless.
a. Find the acceleration of the system and the two
tensions.
b. How would your answers change if there was friction
and the coefficient of kinetic friction between the table
and the blocks was 0.2.

Created by Alexandru Maries 13-7

Review problems
B. An amusement park ride carries patrons dressed as pirates around in a
big vertical water wheel (radius 7.3 m). The wheel spins so fast (13.2
m/s) that the pirates can stand with their heads pointed inward for the
entire circle. Find the force the ride exerts on a pirate of mass 85 kg both
at the top and at the bottom of the ride.

 Compare your answers to your group before proceeding. Consult with your TA if consensus cannot be reached.

Created by Alexandru Maries 13-8