The Sears Tower in Chicago is 1450 ft tall from its roof to the ground. Markus takes a baseball to the roof, and somehow gets it out of the window with no force imposed on it. Now the ball falls freely toward the ground. Assuming the air has no significant influence on the baseball and the gravitational acceleration in Chicago is 32 ft/s2, Markus wonders, without using calculus:
How fast is ball falling?
How does the distance from the roof to the ball change over time?
When the ball hits on the ground, how fast is it moving at that moment?
Would it hurt if it happened to drop on someone’s foot?
In the following applet, note that the point "Distance" related "time" to the "area of the shaded region," that is, it traces the change of distance over time. What does it look like?
Questions for reflection:
How is the mathematical model different than the real-world scenairo?
What would you do if someone insists on using a vector to describe the speed (negative in this case)?
What if Markus throws the ball horizontally before letting it out of hand?