(scenario from Chain of Evidence by Ridley Pearson)
Objective: Students will learn about physics and projectile motion through modeling the path of an object.
Materials: Each student will need
In this novel, Joe Dartelli is a detective investigating an apparent suicide. He is meeting with Teddy Bragg, a forensic scientist to discuss his findings. Read the excerpt from the book below. Use the information to build a computer model that demonstrates whether the victim, David Stapleton, fell or was pushed from his hotel window.
"One big difference between the laws we both deal with. Yours are made by man and they vary all the time according to courts and juries. Mine are laws of nature, and they don't vary an iota. I can't make them vary, even should I want to - and sometimes I want to real bad." He slapped the space bar dramatically, and the screen came alive with color. It took Dartelli a moment to see that he was looking from above, down the face of a building at a sidewalk. It was done in computer graphics, and though realistic, it did not look like anything Dartelli had seen: not quite a photograph, not quite a drawing.
"I know this place," Dartelli said.
"The De Nada," Bragg informed him. "The particular laws I'm referring to are the laws of physics. They dictate the rate at which an object will fall. You can't screw around with that, no matter what. This is a three-D modeled visualization program-computer animation but governed by the laws of physics. How fast and at what angle of trajectory an object falls determines where it lands - pretty simple. In this case, vice versa-we know where Stapleton landed. We measured it. We photographed it. We documented it every way available to us - and that's considerable. Doc Ray's pathology report tells us that wounds on Stapleton indicate that he struck that giant cement pot before he landed - one of those pots designed to keep trucks from driving into the lobby, although at the Granada Inn I think that might be an improvement."
Dartelli felt obliged to chuckle, though he felt a little tense for this reaction.
Bragg went on. "That pot is a fair piece of change away from the wall, which is what got me interested in the first place." He glanced at Dartelli - he had mischief in his eyes. "Enough of my flapping," he said. "I'll let my fingers do the talking."
The screen changed to a color photograph. Bragg told him, "This is from inside Stapleton's hotel room." He hit some more keys and the photograph faded away, replaced by an exact replica in computer three-dimensional graphics.
"Nice," Dartelli said.
"Slick piece of software," Bragg agreed. "But notice the restrictions. Place is a sardine can. Foot of the bed practically hits the dresser; you can't even open the bottom drawer all the way - I tried that, remember. "Enter David Stapleton." He touched a few keys and a three-dimensional stick figure appeared in the room, looking like an undressed mannequin. "The animation lets us interact with Stapleton's possible trajectories in a scientifically accurate model," he emphasized for Dart's sake. Gragg revered science the way theologians talked of God.
He worked the keyboard again, returning Dartelli and the screen to the outside, this time from the sidewalk perspective where a crime-scene photograph showed a bloodied Stapleton folded on the sidewalk. He once again manipulated the system into performing a metamorphism between the photographic image and one that was the result of computerization. Stapleton transformed into that same white mannequin.
"We work backward." He controlled the software so that the mannequin slowly unfolded itself, lifted off the sidewalk, connected with the rim of the enormous cement pot, and then floated up into the air, feet first, head pointed down toward the earth. Dartelli recalled the black kid's description of Stapleton diving out the window, the kid whistling as he waved his large hand in the air indicating the dive.
Bragg said, "The specific trajectory allows us to compute the velocity necessary to launch Stapleton out the window in order for him to travel the distance he actually traveled. Any other velocity, and he lands in a different spot, connects with that pot differently, or misses it altogether.
"Then," Bragg added, "we look at three different scenarios: stepping off the windowsill, running at the window and diving, or...being thrown."
Dart's breath caught and heat spiked up his spine. The chair wavered and nearly went over backward; he caught his balance at the last possible second.
"We ask for new chairs," Bragg said, "but we never get them."
....
"We have his weight programmed into it, his height. If he had an extraordinary build I might tweak things to make him appear stronger to the software. So let's make him run for that window." The software showed the mannequin attempt to run through the room for the window. The tight quarters required an awkward sidestepping. "You should have seen us trying to convince the thing to do that dance," Bragg said. The mannequin struck the window, and fake pieces of glass went out with him. "We tried ten different times to get him out that opening with the speed necessary. He went through the glass every time. Turns out he would have had to start the dive back by the bed to make it out that opening with the necessary speed. That computes to traveling three feet, perfectly level through the air - Superman maybe, not David Stapleton."
Modeling Stapleton's "fall"
Have your students use a spreadsheet program such as Excel to demonstrate the two other scenarios for Stapleton's fall.
Useful Equations