Vertical Motion and Free Fall - Online Tutor, Practice Problems & Exam Prep

Vertical motion problems are solved using the same principles as horizontal motion, focusing on free fall where gravity is the only acting force. Objects in free fall experience a constant acceleration of g=9.8m/s². When analyzing these problems, it's essential to identify five variables, using Δy for displacement and v for velocity. The acceleration a is typically negative when the upward direction is considered positive, simplifying calculations.

Vertical Motion & Free Fall

Hey, guys. You're going to need to know how to solve problems where things are moving up or down on the vertical plane rather than on a flat horizontal surface. This is called vertical motion. And in this video, we're going to see that vertical motion problems are solved using the exact same steps and the exact same equations as we did for horizontal motion. So let's check it out. But first, I actually want to talk about free fall because it's something that your professors and textbooks are going to cover. We are going to use it later. So the basic idea of free fall is that objects are in free fall if the only force that acts on them is the force of gravity. So that's the symbol fg, even if these things are moving upwards. For example, let's say we had a box and you were holding that box using some string. Basically, you're applying some tension. Well, the other force that's acting on it is gravity. It wants to pull it down. So you're holding it up using the string, but gravity wants to pull it down. So there are 2 forces acting on this object. Therefore, it's not in free fall. Now what if you were to just let the string go? Well, at that point then, the only force that is acting on it is gravity, and obviously, the box is going to fall to the ground. So that means that you have free fall motion. Now what if, instead of dropping the box or dropping the string, you were to actually throw the box upwards, basically just giving it some initial velocity? Well, it turns out that that doesn't really matter because even though you throw it up, once you let it go, the only force that acts on it is still gravity. So, therefore, it's in free fall motion. It doesn't really matter the fact that it's moving upwards. The only thing that does matter is that the only thing that's acting on it is gravity.

Now the reason this is important is because objects in free fall experience constant vertical acceleration. So an object in free fall experiences a constant acceleration and that's super important because that means we can use all of our UAM equations to solve vertical motion problems. So we're going to use the same list of steps, and we're going to use the same exact equations to solve these things, but there are a couple of differences. So let's go ahead and check it out. With horizontal motion, we always just drew a diagram like this of our problem and then we came up with a list of 5 variables. And then from this list, we needed 3 out of 5. So we need 3 out of the 5 variables in order to be able to pick an equation from this list that didn't have the ignored variable. Well, vertical motion is going to be the exact same thing. You're going to draw the diagram whether it's moving up or down or whatever, and then you're going to come up with your list of 5 variables. And then, basically, from this list here, we need 3 out of 5. So I need 3 out of 5 variables just like I did for horizontal motion to pick a very to pick an equation from this list over here that doesn't have my ignored. So again, the difference really is this that use we use delta x's for horizontal motion. We're going to use delta y's. We use vx, so now we're going to use vy. So basically, everything just gets replaced from x's x's to y's, and so therefore, our equations are instead going to instead of having x's in them, they're just going to have y's.

Now, the other big difference between vertical motion actually has to do with this acceleration term, this ay. So let's check it out. And basically, what's happening is that objects in free fall, in free fall vertical motion, are going to accelerate downwards with a constant vertical acceleration known as the free fall acceleration little g. It's not to be confused with fg. That was the force. This is the acceleration that that force produces. Now what you absolutely need to know about little g is that on Earth, it is always a fixed value of 9.8ms-2. So g is always equal to 9.8, and that's regardless of weight. So that means that if you grab a book and a pencil and if you drop them, they're both going to accelerate downwards at 9.8 ms-2. So what does that mean about our acceleration term? Well, our acceleration term is basically just going to be plus or minus g. So your professors and textbooks are going to use either a positive or negative sign. That really just depends on what the direction of positive is and that's based on your problem. So that just means that ay is always going to be positive or negative 9.8ms-2. We're going to talk about this in just a second, how we actually figure out whether it's positive or negative. So, basically, all this means here is that we're going to use the same exact equations as we did before, but of our variables, of our five variables, we already know what one of them is going to be. It's just going to be 9.8. We just have to figure out whether it's positive or negative. So let's go ahead and take a look at a problem here. We've got a ball we're going to drop from rest from a 100 meter tall building. So let's just go ahead and draw this out. So I've got a building here. I know this is, a 100 meters and I'm going to drop a ball. It's going to fall, and I know I'm dropping it from rest, which means my initial velocity is 0. And I want to calculate the ball's velocity right before it hits the ground. So right at the bottom here, it's going to have some final velocity vy, and that's actually what I'm trying to find. Find. So this is my target variable. So I've already kind of just drawn the diagram. Let's go ahead and list out the other variables that I need. So I've already got 2 of them, Vnaught and Vy. So I need delta y, then I need ay, and then I need delta t. So these are my 5 variables here. So what's my delta y, my displacement? Well, I'm starting from the top of the building and then I'm heading downwards, so that means that my delta y is going to be 100 meters, and then I know my acceleration in the y-direction is going to be either positive or negative 9.8 ms-2. So I've got plus or minus g, which is plus or minu

A rock is thrown vertically upward with a speed of 27.0 m/s from the roof of a 31.0-m-tall building. The rock doesn't hit the building on its way back down and lands in the street below. (a) What is the speed of the rock just before it hits the street? (b) How much time elapses from when the rock is thrown until it hits the street?

• A. (a) vy = 36.6 m/s downward;
  (b) t = 3.88 s
• B. (a) vy = 11.0 m/s downward;
  (b) t = 3.88 s
• C. (a) vy = 37.0 m/s downward;
  (b) t = 34.2 s
• D. (a) vy = 36.6 m/s downward;
  (b) t = 6.49 s

A student throws a set of keys vertically upward to her sorority sister who is in a window 14.00 m above. The second student catches the keys 1.50 s later. (a) With what initial velocity were the keys thrown? (b) What was the velocity of the keys just before they were caught?

• A. (a) v_0y=37.5 m/s
  (b) v_y=22.8 m/s
• B. (a) v_0y=16.7 m/s
  (b) v_y=2 m/s
• C. (a) v_0y=2 m/s
  (b) v_y=0 m/s

Here’s what students ask on this topic:

What is the acceleration due to gravity in free fall?

The acceleration due to gravity in free fall is denoted by the symbol g and has a constant value of 9.8 m/s² on Earth. This means that any object in free fall, regardless of its mass, will accelerate downwards at this rate, assuming no other forces (like air resistance) are acting on it. This constant acceleration is crucial for solving vertical motion problems using the kinematic equations.

How do you determine the direction of acceleration in vertical motion problems?

In vertical motion problems, the direction of acceleration is determined by the choice of the positive direction. If you choose the upward direction as positive, then the acceleration due to gravity a_y will be negative, i.e., -9.8 m/s². Conversely, if you choose the downward direction as positive, then a_y will be positive, i.e., 9.8 m/s². Consistently applying this choice simplifies calculations and helps avoid confusion.

What are the key variables used in solving vertical motion problems?

The key variables used in solving vertical motion problems are: initial velocity (v₀), final velocity (v), displacement (Δy), acceleration (a_y), and time (t). These variables are used in the kinematic equations to solve for unknowns. For vertical motion, displacement is denoted as Δy and acceleration is typically ±9.8 m/s² depending on the chosen positive direction.

How do you solve for the final velocity of an object in free fall?

To solve for the final velocity (v) of an object in free fall, you can use the kinematic equation: $v^2=v^0+2ay\mathrm{\Delta y}$. Here, v₀ is the initial velocity, a_y is the acceleration due to gravity (typically -9.8 m/s² if upward is positive), and Δy is the displacement. Plug in the known values and solve for v.

What is free fall and how does it differ from other types of motion?

Free fall is a type of motion where the only force acting on an object is gravity. This means that the object experiences a constant acceleration of 9.8 m/s² downwards. Unlike other types of motion where multiple forces might be acting (e.g., tension, friction), free fall is characterized by the absence of any force other than gravity. This simplifies the analysis and allows the use of kinematic equations with a constant acceleration.