# 2015 AP Physics 1 Free Response #4

TLDRIn this educational video, Alan Bothell, a STEM coach, explains AP Physics 1 exam response question 4 from 2015. He discusses two identical spheres released from the same height with different initial conditions: Sphere A falls straight down with no initial velocity, while Sphere B has an initial horizontal velocity. Despite traveling different horizontal distances, both spheres hit the ground simultaneously due to identical vertical motions. Alan illustrates this with a Freebody diagram and velocity graphs, emphasizing that horizontal displacement does not affect the timing of the vertical fall. He concludes by offering free homework help on Twitch and Discord for those interested in math and physics.

###### Takeaways

- π Two identical spheres are released from the same height at time T=0.
- π Sphere A has no initial velocity and falls straight down.
- πββοΈ Sphere B is given an initial horizontal velocity (Vβ) and covers more horizontal distance before landing.
- π Both spheres reach the ground at the same time (T_f), despite different horizontal distances traveled.
- π The only force acting on the spheres at T_f is gravity, as air resistance is negligible.
- π Sphere A has no horizontal velocity, while sphere B maintains a constant horizontal velocity (Vβ) until it hits the ground.
- π Both spheres have the same vertical motion, starting with zero vertical velocity and accelerating downwards due to gravity.
- π The horizontal displacement of sphere B does not affect the time it takes to reach the ground.
- π The vertical distance traveled by both spheres is the same, leading to the same time to fall.
- π The video's main takeaway is that horizontal motion does not influence the time it takes for objects to fall if air resistance is negligible.

###### Q & A

### What is the topic of the video?

-The video is about continuing the discussion on the 2015 AP Physics 1 exam, specifically focusing on response question number 4.

### What are the two scenarios described for the spheres in the question?

-The two scenarios are: Sphere A is released with no initial velocity and falls straight down, while Sphere B is given an initial horizontal velocity and travels a horizontal distance before reaching the ground.

### Why do both spheres reach the ground at the same time?

-Both spheres reach the ground at the same time because they fall from the same height and are only acted upon by gravity, which affects their vertical motion equally, regardless of their horizontal motion.

### What is the significance of air resistance in this scenario?

-Air resistance is negligible in this scenario, meaning it does not affect the motion of the spheres and can be ignored in the analysis.

### What is the force acting on Sphere A as it falls?

-The only force acting on Sphere A as it falls is gravity, which acts vertically downwards.

### What is the horizontal velocity of Sphere A throughout its fall?

-Since Sphere A has no initial horizontal velocity, its horizontal velocity remains zero throughout its fall.

### What is the horizontal velocity of Sphere B throughout its fall?

-Sphere B maintains a constant horizontal velocity of magnitude Vβ throughout its fall due to the absence of forces in the horizontal direction.

### What does the free-body diagram represent in this context?

-The free-body diagram represents all the forces acting on an object. In this context, it would show the gravitational force acting on both spheres during their fall.

### How does the horizontal motion of Sphere B compare to Sphere A?

-Sphere B has an initial horizontal velocity (Vβ), causing it to travel a horizontal distance before landing, unlike Sphere A, which does not have any horizontal motion.

### What is the conclusion about the vertical motion of both spheres?

-The conclusion is that both spheres have the same vertical motion, starting with zero vertical velocity and being accelerated downward by gravity at the same rate, resulting in them reaching the ground at the same time.

### What additional resources does the video offer for learning physics?

-The video mentions that the presenter offers free homework help on platforms like Twitch or Discord for those who have questions about homework or want to learn more about math and physics.

###### Outlines

##### π AP Physics 1 Exam Question 4 Analysis

In this paragraph, Alan Bothell, a STEM coach, discusses question number 4 from the 2015 AP Physics 1 exam. The question involves two identical spheres released from the same height at time zero. Sphere A falls straight down with no initial velocity, while Sphere B is given an initial horizontal velocity. Despite traveling different distances, both spheres reach the ground at the same time due to the negligible air resistance. Alan explains the concept of a free-body diagram, labeling the forces exerted on the spheres at the time they hit the ground. He emphasizes that the horizontal velocity of Sphere B remains constant (V naught) until it hits the ground, while Sphere A has no horizontal velocity. The explanation includes a discussion on why both spheres reach the ground at the same time, focusing on the vertical motion and the fact that the horizontal displacement does not affect the timing of the fall.

###### Mindmap

###### Keywords

##### π‘Freebody diagram

##### π‘Gravity

##### π‘Horizontal velocity

##### π‘Vertical velocity

##### π‘Air resistance

##### π‘Identical spheres

##### π‘Initial velocity

##### π‘TF

##### π‘Displacement

##### π‘Vertical direction

###### Highlights

Continuing the 2015 AP Physics 1 exam response questions, focusing on question number 4.

Two identical spheres are released from the same height with different initial conditions.

Sphere A has no initial velocity and falls straight down.

Sphere B is given an initial horizontal velocity of magnitude V naught.

Both spheres reach the ground at the same time despite different trajectories.

Air resistance is negligible in this scenario.

Instructions to draw a Freebody diagram and label the forces exerted at time TF.

The only force on the spheres during the fall is gravity.

Identical spheres imply the same mass, affecting the force of gravity.

Graphing the horizontal component velocity of sphere A and B as a function of time.

Sphere A has no horizontal velocity, while sphere B maintains a constant V naught.

The horizontal displacement does not affect the vertical motion of the spheres.

Both spheres start with the same vertical velocity and acceleration.

The vertical distance traveled is the same for both spheres, regardless of horizontal motion.

Sphere B travels further horizontally due to its initial velocity.

The horizontal displacement does not affect the timing of the ground impact.

The answer key suggests a straightforward understanding of the problem.

Offering free homework help on Twitch or Discord for further learning and questions.

###### Transcripts

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