Two Dimensional Motion

AP Physics

Mr. Porter

Freefall

  • An object in freefall is on object which is only acted on by the force of gravity
  • Therefore, it accelerates at
  • is known as the acceleration due to gravity
  • But is best to be called gravitational field strength
  • Direction of is towards the center of the planet (down)

Value of

  • On Earth it is about m/s
  • This varies based on your distance from the center of the Earth, but doesn't vary much beyond to m/s.
  • On quizzes and test including the AP Exam we will round this to m/s to allow for faster calculations.
    • You will not be marked incorrect for using 9.8 m/s
  • Physics Classroom website, which I often use for HW will use 9.8 m/s

Freefall Problems

  1. A ball is released from rest from an elevated position and free-falls towards the ground. Assuming negligible air resistance, what is the ball's speed after 4.5 seconds?
  2. A ball is released from rest from an elevated position and free-falls towards the ground. If it strikes the ground after 3.0 seconds, then what was the height from which the ball was released? Assume negligible air resistance.
  3. A tennis ball cannon projects a ball vertically upward with an initial speed of 50 m/s. Assuming negligible air resistance, with what speed will the ball be moving after 3.0 seconds.

Free Fall Derivation

Derive an expression for the amount of time it takes an object to fall a vertical distance when dropped (released from rest).

Horizontal Projectiles

Two toy trucks roll off the ends of identical tables. The speeds and masses of the trucks are given.

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Will Truck A be in the air for (i) a longer time, (ii) a shorter time, or (iii) the same time as Truck B before it reaches the floor?

Explain your reasoning.

Two toy trucks roll off the ends of identical tables. The speeds and masses of the trucks are given.

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Will Truck A be in the air for (i) a longer time, (ii) a shorter time, or (iii) the same time as Truck B before it reaches the floor?

Explain your reasoning.

Launcher Demo

Horizontal Projectiles

  • A projectile is an object that only experiences a gravitational force
  • For horizontal projectiles the
  • We can separate motion in the and planes and solve separately

Horizontal Projectils

X-Plane Motion

  • is constant

Y-Plane Motion

  • constant acceleration

Double Cross Diagram

Practice

In many locations, old abandoned stone quarries have become filled with water once excavating has been completed. While standing on a quarry wall, a boy tosses a piece of granite into the water below. If he throws the rock horizontally
with a velocity of 3.0 m/s, and it strikes the water 4.5 meters away, how high above the water is the wall?

Practice w/ Table

Suppose that an airplane flying 60 m/s, at a height of 300 meters, dropped a sack of flour. How far from the point of release would the sack have traveled when it struck the ground? Where will the plane be in relation to the sack when it hits the ground?

Marble Mini-Experiment

  1. Determine the launch velocity of your marble.

Equipment:

  • Ruler track
  • Marble
  • Carbon paper
  • Meterstick
  1. Use to predict landing spot from new height (like off top of cabinets)

Rank the situations from the greatest to least time that it will take for the sphere to hit the ground. Make your ranking on a single line, using > and = signs. Ties are possible.

Rank the situations from the greatest to the least horizontal distance that the sphere will travel. Make your ranking on a single line, using only the > and = signs. Ties are possible.

Projectiles

Fired at an Angle

Velocity as a 2-Dimensional Vector

Vector Components

Finding Vector Components

Practice:

Find the x & y components of the following velocities...

  1. A water balloon is launched with a speed of 40 m/s at an angle of 60 degrees to the horizontal.
  2. A motorcycle stunt person traveling 70 mi/hr jumps off a ramp at an angle of 35 degrees to the horizontal.
  3. A springboard diver jumps with a velocity of 10 m/s at an angle of 80 degrees to the horizontal.

Some Projectile Reminders & Facts:

  • When an object is in free-fall,

    • its VERTICAL acceleration is always or near the surface of the earth.
    • its HORIZONTAL acceleration is always zero. Meaning the only equation you use for the horizontal motion is

  • Velocities in perpendicular directions add with the Pythagorean theorem

  • The magnitude of an object's velocity is known as its speed

  • To approach a projectile problem, make two kinematics charts: one vertical, one horizontal.

Concept Checker 🤔 ✔️

A baseball is thrown from point S in right field to home plate.

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Use a coordinate system with up (+x) and left (+y), and the origin at home plate.
Select the graph that best represents:

  1. vs.
  2. vs.
  3. vs.
  4. vs.




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An airplane is flying 1200 m above the ground at a speed of 200 m/s. It drops a bag that hits the ground after traveling a horizontal distance of 3130 m.

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  1. The plane’s speed is tripled.
  2. The plane is climbing straight up.
  3. The plane is flying level at an altitude of 1,100 m.
  4. The mass of the bag is increased.
  5. The bag is thrown from the plane with a of 15 m/s down.

(i) The will be greater than 3130 m.
(ii) The will be less than 3130 m but not zero.
(iii) The will be equal to 3130 m.
(iv) The will be zero
(v) We cannot determine how this change will affect .

Problem-Solving Approach

  1. Find and
  2. Make double cross diagram & determine problem solving approach
    • often involves finding flight time first
  3. Solve

Together

A long jumper leaves the ground with an initial velocity of at an angle of above the horizontal.

Determine

  1. the time of flight
  2. the horizontal distance
  3. the peak height of the long-jumper

Practice Time

Turd the Target 💩

Frames of Reference

Relative Velocity

Headwind and Tail Wind

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Images from Physics Classroom

Cross Wind...

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Animation

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Classic Physics Problem Riverboat

A motorboat traveling 4 m/s, East encounters a current traveling 3.0 m/s, North.

  1. What is the resultant velocity of the motorboat?
  2. If the width of the river is 80 meters wide, then how much time does it take the boat to travel shore to shore?
  3. What distance downstream does the boat reach the opposite shore?