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### 307-I: Horizontal Launch 1: Numeric Analysis

• Topic Cluster: Kinematics
• Topic: Projectile Motion
• Objective: Solve for important kinematic quantities when an object is launched horizontally.
• Content: When an object is launched horizontally, it moves at a constant speed in the horizontal dimension and accelerates downward in the vertical dimension; physicists can use the kinematic equations to analyze the motion of this object.
• Level: 3

#### BACK to Ladder Projectile Motion

Our ultimate goal is to analyze the motion of any object that is fired into the air. In this section, we will consider a specific case of a projectile: cars that drive off of cliffs! These problems are simpler than a object fired upwards or downwards, but In this section, we will explore problems in which an object is fired from some height with horizontal velocity. In this event, we will need to use the principle of two-dimensional motion.

##### Principle of Two Dimensional Motion

When an object is moving in two dimensions, the motion in one dimension does not affect the motion in the other dimension.

#### Table for Organizing Horizontal Launch Problems

Horizontal Motion
Vertical Motion
Description of Motion
Moving forwards at a constant velocity
Accelerating downwards at a rate or 9.8 m/s/s
Formulas
• $$\Delta x = v_x \cdot \Delta t$$
• $$v_{fy} = v_{iy} + a_y \cdot \Delta t$$
• $$\Delta t = v_{iy} \cdot \Delta t + \frac{1}{2} a_y$$
• $$\Delta y = \left( \frac{v_{iy} + v_{fy}}{2} \right) \Delta t$$
• $$v^2_{fy} = v^2_{iy} + 2 a \cdot \Delta x$$
Quantities
• $$\Delta x =$$
• $$v_x =$$
• $$\Delta t =$$
Quantities
• $$\Delta y =$$
• $$v_{yi} =$$
• $$v_{yf} =$$
• $$a_y =$$
• $$\Delta t =$$
1. A car drives off of a cliff that is 30 meters tall at a horizontal speed of 15 m/s. How far does it travel before striking the ground?
Here is how the information translates into physics quantities:
• The horizontal velocity is 15 m/s. This is the speed the car was going when it went off the cliff.
• The initial vertical velocity is 0. The car is not moving vertically when it flies off the cliff.
• The vertical displacement is -30 m. This is how far it travels vertically before striking the ground. This value is negative because the displacement is downward.
• The vertical acceleration is -9.8 m/s2. This value is negative because the acceleration is downward.
• The quantity that the problem is looking for is horizontal displacement.

Use the table above to find all of the unknown quantities.
Write the final answer (the horizontal displacement) here:
2. A car drives off of a cliff that is 50 meters tall at a horizontal speed of 20 m/s. How far does it travel before striking the ground?
Here is how the information translates into physics quantities:
• The horizontal velocity is 20 m/s. This is the speed the car was goign when it went off the cliff.
• The initial vertical velocity is 0. The car is not moving vertically when it flies off the cliff.
• The vertical displacement is -50 m. This is how far it travels vertically before striking the ground. This value is negative because the displacement is downward.
• The vertical acceleration is -9.8 m/s2. This value is negative because the acceleration is downward.
• The quantity that the problem is looking for is horizontal displacement.

Use the table above to find all of the unknown quantities.
Write the final answer (the horizontal displacement) here:
##### Less Guidance
1. A car drives horizontally off a cliff with a speed of 24.0 m/s. The cliff has a height of 30.0 meters. Determine:
1. The time before the car strikes the ground.
2. The vertical speed at which the car strikes the ground.
3. The distance that the car travels before striking the ground.
2. A car drives horizontally off a cliff with a speed of 18.5 m/s. The cliff has a height of 6.8 meters. Determine:
1. The time before the car strikes the ground.
2. The vertical speed at which the car strikes the ground.
3. The distance that the car travels before striking the ground.
##### Conceptual Questions
1. Why are there four equations available to use in the vertical dimension, but only one available in the horizontal dimension?
2. Which is the only quantity that is the same in both dimensions? Why?
3. Why are the velocity and acceleration in the vertical dimension negative?

Coming soon!

Coming soon!

### Resources

#### AP Physics 1 Topic 1.1: Daily Video 8 (Skill 2.1)

Classroom Daily Videos are not available year round. The release dates for each video this page. AP Classroom Daily Videos are available only to students in AP Physics.