Example problem — Projectile motion

When I wrote how I plan to make exam questions un-googleable, what I probably should have said was less googleable. Let’s go with that instead.

Let’s try an example of a problem that is “less googleable”. Here’s what I want to start with:

Problem: Lisa throws a stone horizontally from the roof edge of a 50.0 meter high dormitory. It hits the ground at a point 60.0 m from the building. Find the time of flight.

This problem is actually quite googleable, and I’m quite certain the solution and answer are all over the internet. But, just to be sure, here’s my solution and answer:

But, I wouldn’t be asking for the solution to the problem. Instead, I might ask for the following:

1. Motion diagrams
2. Graphs of position vs. time, velocity vs. time, acceleration vs. time

I might also ask for student to:

• Explore the range of possible values for given quantities.

For this example, I’m going to look at the range of values that the stone might be able to go horizontally. If there is no initial velocity in the horizontal direction, the stone falls straight down, and the horizontal distance is zero. That’s not super interesting, although it is what happens at one extreme.

To increase the distance the stone goes horizontally, we need to either increase the initial speed of the stone or make the building taller, or both. I imagined a major league pitcher on top of a building, and assumed the pitcher could throw the stone 90 miles per hour. Then, I replaced the building in the problem with the world’s tallest building, the Burj Khalifia in Dubai, with a height of 828 m. Assuming(!) air resistance can be ignored this is what I find:

It’s probably not reasonable to assume that the air resistance can be ignored from that height, but for our purposes, this is an interesting result.

If I were giving this problem to students, I would also want them to comment on what they thought the main point of the problem was. In my mind, one of the main take aways from this problem is that it demonstrates how a projectile motion problem can be approached by separating the horizontal motion from the vertical motion. For this problem, and for many others like it, the time in the air is determined only by the motion in the vertical direction. Once we knew the time the stone was in the air, finding the horizontal range required knowing the horizontal component of the velocity and recognizing that component doesn’t change. As showed with the motion diagrams and graphs, there was no acceleration in the horizontal direction.