Physics: 2D & Vectors
Review Guide
𝑣𝑥 =
𝑑
𝑡
Name________________________________
1
2 3
4 5 6 7
8
𝑣𝑓 = 𝑣𝑖 + 𝑎𝑡
1
1
Δ𝑥 = 𝑣𝑖 𝑡 + 𝑎𝑡 2
Δ𝑥 = (𝑣𝑖 + 𝑣𝑓 )𝑡
2
2
𝑎𝑑𝑗
𝑜𝑝𝑝
cos(𝜃) =
tan(𝜃) =
ℎ𝑦𝑝
𝑎𝑑𝑗
𝑣𝑓2 = 𝑣𝑖2 + 2𝑎(Δ𝑥)
sin(𝜃) =
𝑜𝑝𝑝
ℎ𝑦𝑝
1. Oceanic Airlines Flight 815 flies with a velocity of 250 m/s east. If the plane flies through a crosswind
of 25 m/s from north to south, what is the resultant velocity of the plane? (Magnitude and direction!)
2. James Ford swims with the current of a river that flows with a velocity of 3 m/s north. If James
swims with a velocity of 2 m/s, what is his resultant velocity?
3. Use the vectors below to answer a-e.
a. What is the resultant of 1 + 3?
d. What is the resultant of 1 + 2?
b. What is the x-component of 5?
e. What is the resultant of 2 + 3?
c. What is the y-component of 4?
4. Two vectors of length 14 and length 16 are added together. The result will never be less than two no
matter what direction the vectors point. Why?
5. A skateboarding salamander rolls off the side of a cliff that is 25 m tall. Draw a picture of the
salamander’s adventure below. Be sure to show the path the salamander takes. What is this shape
called?
6. What angle would you launch something if you want it to have…
a. Max horizontal velocity?
d. Longest time of flight?
b. Max vertical velocity?
e. Longest horizontal distance?
c. Maximum height possible?
7. In a fit of rage, Johnny Tsunami throws his surfboard off a cliff! He throws the surfboard at an angle,
as shown in the picture below. On the picture, label…
a. When the surfboard has the maximum vertical velocity.
b. When the surfboard has the minimum vertical velocity.
c. When the surfboard has the maximum horizontal velocity.
d. When the surfboard has zero vertical velocity.
e. When the surfboard isn’t moving.
8. In class, you saw that a quarter that is launched horizontally will hit the ground at the same time as
quarter that is dropped. Why?
9. Break the following three vectors into x and y components.
a. 25 m @ 35° N of E
b. 12 m/s @ 22° W of N
c. 88 mph @ 45°N of W
10. Add the following vectors: 25 m N, 35 m E, and 40 m @ 75°E of N.
x
y
Magnitude and Direction
11. While running an out route, a receiver runs 10 m up the field and 2 m “out” (toward the sideline).
What is the displacement of the receiver? (Magnitude and direction!)
12. A baseball is thrown with a velocity of 35 m/s at an angle of 25°. The ball is thrown from third to
first, a distance of 38.7 m. How much time does it take the ball to reach first base?
13. Artie, the strongest man in the world, rolls a boulder off a cliff with a velocity of 12 m/s. The cliff is
25 m tall. How far from the base of the cliff does the boulder land?
14. While listening to his favorite CD, Through Being Cool by Saves the Day, Landon decides to throw a
football horizontally off his roof. The football lands 12 m from the base of the house, and the roof is
6 m from the ground. With what velocity did Landon throw the football?
15. Max the leaping dog can jump with a velocity of 12 m/s. If Max jumps at an angle of 60°, can he
clear a hurdle that is 4 m high?
16. It’s common knowledge that hockey is the best sport ever. Zdeno Chara has a slapshot that leaves his
stick at 48.2 m/s. If the puck leaves his stick at a 12° angle, what will the horizontal and vertical
velocities of the puck be when it comes back to the ground?
17. Malicious Mary is extremely upset with her computer! She decides to throw the computer
horizontally off a cliff with a velocity of 8 m/s. If the computer lands after 2.56 s, how tall is the
cliff?
18. A rampaging rhino runs across a river! The rhino runs with a velocity of 4 m/s, and the river flows
with a velocity of 4 m/s. What is the resultant velocity of the rhino? (Magnitude and direction!)
19. An incompetent referee thinks he sees a stupid holding penalty, so he decides to throw his flag
horizontally. He throws the flag from 1.5 m in the air, and he needs the flag to land 6 m away from
him. With what velocity must he throw the flag?
20. A cannonball is launched at an angle. As the cannonball flies through the air, describe what happens
to the…
a. Horizontal velocity
b. Vertical velocity