The two positive times in projectile motion refer to the time it takes for the object to reach its maximum height (vertical motion) and the time it takes for the object to return to its original height (horizontal motion).
So to answer another question, I delved into python + pygame projectile motion. Basically I wanted to create a sprite, then when "launched" with an initial velocity and angle would behave as per gravity and Newtonian physics.
One of the powers of physics is its ability to use physics principles to make predictions about the final outcome of a moving object. Such predictions are made through the application of physical principles and mathematical formulas to a given set of initial conditions. In the case of projectiles, a student of physics can use information about the initial velocity and position of a projectile to predict such things as how much time the projectile is in the air and how far the projectile will go. The physical principles that must be applied are those discussed previously in Lesson 2. The mathematical formulas that are used are commonly referred to as kinematic equations. Combining the two allows one to make predictions concerning the motion of a projectile. In a typical physics class, the predictive ability of the principles and formulas are most often demonstrated in word story problems known as projectile problems.
A projectile is launched at an angle to the horizontal and rises upwards to a peak while moving horizontally. Upon reaching the peak, the projectile falls with a motion that is symmetrical to its path upwards to the peak. Predictable unknowns include the time of flight, the horizontal range, and the height of the projectile when it is at its peak.
The above equations work well for motion in one-dimension, but a projectile is usually moving in two dimensions - both horizontally and vertically. Since these two components of motion are independent of each other, two distinctly separate sets of equations are needed - one for the projectile's horizontal motion and one for its vertical motion. Thus, the three equations above are transformed into two sets of three equations. For the horizontal components of motion, the equations are
Everytime I approach any projectile motion/kinematics problem, I get confused. I don't know how to translate the problem into an operational method, and every time I complete a problem, the next one is a new mystery to me.
But how to check my class's conceptual understanding? Knowing what kinematics calculations mean is ultimately as important as being able to do the calculations to begin with. In that spirit, here's a different sort of projectile question, the kind that's rare to see as an end-of-chapter exercise. Not a single calculation is necessary, yet I'd in no way categorize it as easy compared with typical AP questions.
How can you measure the horizontal and vertical velocities of a projectile? Vernier's Logger Pro can import video of a projectile. From the video, you can produce graphs and calculations of pretty much any quantity you want. Experimentally verify the answers to the AP-style problem above. Take video of two balls, perhaps launched with a Pasco projectile launcher so they are guaranteed to have the same initial speed. Launch one ball straight up, the other at an angle. Import the video to Logger Pro. Then check to see whether the speed of each ball is in fact the same at a given height.
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