23 Free Fall
Last chapter, we learned that Earth pulls down on every object on Earth. While the force of gravity pulls differently on different objects — heavy objects are being pulled harder than light objects — the acceleration of all objects is the same. This resulted in our first law of gravity, which tells us that the gravitational force of Earth on an object is given by 
.
When an object is subject to the force of gravity alone, we say the object is in free fall. Below, we will use our brand new theory of gravity to solve problems concerning objects in free fall.
Exercise 23.1: Falling Elevators
Earlier in this book we noted that the fastest elevators in the world were those at the Shanghai tower. They rise 580 m in 55 s. If one of these elevators were to fall from the top of the elevator shaft, how long would it take for the elevator to hit the floor?
If you need it, you can see my solution below. Try going as far as you can before peeking, and only peek at the step at which you’re currently in.
We’ll do one more exercise. Before doing so, however, I need to establish a fact we will end up using when solving the next problem.
Exercise 23.2: Maximum Height
An object is moving up, reaches a maximum height, and then starts moving down. What is the velocity of the object when it reaches it maximum height?
You can in principle solve this problem using calculus, but I think it is much more gratifying to reason this out in English. See if you can figure it out before revealing the answer. I’ve added a hint if you’re feeling stuck.
The above result is something you should remember:
At maximum height, the vertical velocity of an object is zero.
Note this is not a statement about gravity: I never told you what forces are influencing the object’s motion. All you know is that the object reaches a maximum height. That said, this is a useful fact that we can use when solving problems for objects in free fall. In fact, let’s try it now!
Exercise 23.3: Tossing a Ball
You have a ball of mass 
which you throw straight up with an initial speed 
. Find how high the ball goes, and the time that it takes for the ball to get there. You can ignore air resistance (this will always be true for this class unless specifically stated otherwise).
See if you can solve the problem following our usual template. If you get stuck, you can peak at my answer.
Without doing algebra, argue that the amount of time that it takes for the ball to go up is the same as the amount of time that it takes for the ball to go down.
Before we end, I would like to share with you a video that I think beautifully illustrates this fact we discovered above that the velocity of an object at the top of its motion is zero. Check it out.
The video shows Taylor Tries juggling from above. Can you explain why the balls seem to “hover” in place?
Key Takeaways