2016 AP Physics 1- Algebra! Chapter 3

Pointing the way!

1. Write an A if you agree with the statement. Write a D if you disagree with the statement.

Before
Agree or Disagree / Motion / After
Agree or Disagree
Distance and displacement are the same thing
A thrown football follows the hypotenuse of a triangle for its path.
A current of water can speed up, slow down or change the direction of a boat.
Astronauts are weightless while in orbit around the Earth in the ISS because there is very little gravity there.

2. What is a scalar?

3. What is a vector? How do you write a variable to indicate it is a vector?

4. Circle the terms below that are vectors

Displacement distance speedvelocityacceleration

Time temperaturemassaverage velocity

5. Adding parallel vectors

  1. What is the total displacement?
  1. What is the total displacement?


6. The water used in many fountains is recycled. For instance, a single water particle in a fountain travels through an 85 m system and then returns to the same point. What is the displacement of a water particle during one cycle?

7. Adding Parallel vectors : Arlo throws a sphere on a bus.

a. According to Arlo he throws a sphere with a velocity of 10 m/s. How fast do the students on the bus say he threw the sphere?

b. Alice is standing as the bus goes by with a velocity of 15 m/s to the right. How fast does Alice think the sphere is going?

8. Alice and Arlo canoe downstream (with the current). Their speed relative to the banks of the river averages 1.23 m/s. During the return trip they paddle upstream, averaging 0.67 m/s relative to the riverbank.

  1. What is their paddling speed in still water?
  1. What is the speed of the current in the river?
  1. How far do they travel down stream in an hour? Upstream?

9. Applying : Arlo is driving at 50 km/h, while Alice is driving at 30 km/h. They start driving at the same point. How far apart are the cars after 4 hours?

10. Adding perpendicular vectors graphically: Tip-to-Tail

What is the total displacement? What is the total distance traveled?

Now 2 dimensional!

11. Arlo’s boat is heading due South (or at least that is the way it is pointed) as it crosses a wide river with a velocity of 10.0 km/h relative to the water. The river has a uniform velocity of 5.00 km/h due west. Determine the velocity of the boat with respect to an observer on the riverbank.

  1. In a story problem what does it mean if you see “velocity of the boat relative to the water” or “velocity of airplane relative to the air”?
  1. In a story problem what does it mean if you see “velocity of the boat relative to shore” or “velocity of an airplane relative to ground”?
  1. Draw a velocity triangle and a displacement triangle for this scenario.
  1. What is the speed of the boat according to the shore?
  1. How long would it take for the boat to cross a 20 km river?
  1. How far downstream does Arlo end up?

12. Alice rows a boat at 8 km/h directly across a river that flows at 6 km/h.

a. What is the resultant speed of the boat?

  1. How much time does it take Alice to cross the river if it is 10 km across?
  1. How far downstream does Alice end up if the river is 10 km across?

13. Arlo rows a boat at 8 km/h directly across a 10 km wide river that flows at 6 km/h. What if Arlo is trying to get to a point directly across on the shore? What direction should he head?

a)Could Arlo head directly across the river? Where would he end up?

b)Which general way should he head to reach his goal? Draw a velocity and a displacement triangle for this scenario.

c)What is the speed of the boat according to the shore?

d)How long would it take for the boat to cross the river?

e)Find the actual angle at which Arlo must point his boat so his final destination is directly across the river.

14. Arlo wants to go directly across a river that is flowing at 5 km/h south.

a)If his motor is 12 km/h, at what angle should he point his boat to go from the west bank to the east bank?

b)What is the speed of the boat according to the shore?

c)If the river is 10km wide, how long does it take for the boat to cross the river?

Projectile Motion: 2D Free Fall!

  1. What would happen on planet NARANG if a sphere was launched at an angle into the vacuum?
  1. What would happen if you launcheda sphere at an angle into the air on the Moon?
  1. What would happen if you launched a sphere at an angle into the atmosphere on Jupiter?
  1. What force acts on an object in the air here on Earth?
  1. What is the direction of that force/acceleration? What does this tell me about the horizontal motion?
  1. Why is the path a parabola and not a triangle like boats and airplanes?

Horizontal Motion (x-axis) / Vertical Motion (y-axis)
Acceleration magnitude?
Velocity at the top?
Equations that apply?
  1. A steel sphere is launched horizontally with a speed v from the top edge of a table of height h above a level floor. At the same instant, another steel sphere is dropped from the edge of the same table.
  2. Which sphere strikes the floor first?
  3. The sphere launched horizontally
  4. The sphere dropped
  5. The spheres land at the same time

Explain Result:

  1. What is the horizontal motion of the fired sphere? Why?
  1. Model a sphere thrown horizontally. Sketch the path of a sphere and draw arrows showing its horizontal and vertical velocity at three points along the path. Vary the length of your arrows to show the magnitude of the velocities.
  1. Which sphere is traveling faster when it hits the ground? Why?
  1. Does the mass of the spheres matter? Why or why not?

8. How could you find the instantaneous velocity at any point in the motion if you know the horizontal velocity magnitude and the vertical velocity magnitude at that instant?

9. Alice throws a sphere horizontally off a 20 meter cliff with a horizontal speed of 10.0 m/s.

a. What is the time in the air?

Horizontal vertical

b. What is the velocity just before it hits the ground (this includes direction)?

c. What is the horizontal displacement?

10. What if we could launch a horizontal projectile so fast that the Earth curved away as it fell towards the Earth? What’s that called?

  1. Why are astronauts weightless?

11. A projectile is launched at an angle from level ground.

  1. Horizontal velocity
  2. Vertical velocity
  3. Horizontal acceleration
  4. Vertical acceleration
  5. Angle at which the projectile is launched
  1. Which of the above choices is NOT constant throughout the flight of the projectile?
  1. Which of the above choices is zero throughout the flight of the projectile?
  1. Which of the above choices changes direction during the flight of the projectile?

12.

13. A battleship simultaneously fires two shells at enemy ships. If the shells follow the parabolic trajectories shown, which ship gets hit first?

14. Arlo kicks a football with a velocity of 12.8 m/s at an angle of 38 degrees with the horizontal.

  1. What is the time that the football is in the air?

XY

  1. What is the football’s displacement in the horizontal direction?
  1. What is the maximum height that the football will reach?
  1. What is the total velocity just before the ball hits the ground?

15. A projectile is fired with initial velocity vo at an angle 0 with the horizontal and follows the trajectory shown above. Which of the following pairs of graphs best represents the vertical components of the velocity and acceleration.v and a, respectively, of the projectile as functions of time t?

16. What would the graphs look like for the horizontal componentsof the velocity and acceleration as a function of time?

17. A daredevil decides to jump a canyon. Its walls are equally high and 10 m apart. He takes off by driving a motorcycle up a short ramp sloped at an angle of 15 degrees. What minimum speed must he have in order to clear the canyon?

XY

18. What if you wanted to launch a banana to a hungry monkey in a tree but unfortunately the sound of the launch scares the monkey so he lets go the moment you fire. Where would you aim so the monkey could catch the banana mid fall?

a. Above

b. Below

c. At

Explain demonstration

Adding Multiple Vectors!

1. While Arlo plays football he runs 20 yards downfield, then cuts towards the sideline running 15 yards and finally has to cut back 4 yards catching the football. After catching the football Arlo spins around and sprints 25 yards into the end zone!

a. What is his displacement?

b. What is his total distance traveled?

2. Adding vectors graphically that are not parallel or perpendicular

Tip-to-Tail

Try adding the two vectors in a different order. Does it matter?

3. Component Method for adding a bunch of vectors (VERY IMPORTANT!!!)

An ant travels 2cm at a 60 degree angle. It then travels 3 cm at a 230 degree angle. Next the ant travels 5cm at 40 degrees and then finally 1cm at 350 degrees.

Find the ant’s displacement.

Draw a coordinate system for each vector so that each tail is at an origin.

Algebraically determine the resultant displacement: (Watch your signs!)

x-component / y-component
1
2
3
4
Total

Draw the final x vector and the final y vector tip-to-tail.

Find the magnitude of the resultant using the Pythagorean Theorem

Find the direction of the result using tan-1, make sure you draw the final triangle and label the hypotenuse and angle with the tail of the hypotenuse.

4. Find the sum of these four vector forces: 12 N to the right at 35 degrees above the horizontal, 31 N to the left at 55 degrees above the horizontal, 8.4 N to the left at 35 degrees below the horizontal, and 24 N to the right at 55 degrees below the horizontal.

5. A man pushing a mop across a floor causes the mop to undergo two displacements. The first has a magnitude of 150 cm and makes an angle of 120 degrees with the positive x axis. The resultant displacement has a magnitude of 140 cm and is directed at an angle of 35 degrees to the positive x axis. Find the magnitude and direction of the second displacement.