Given the adhere time and ambit catholic of a football, bulk out how aerial it went, how fast you kicked it, and the bend at which it larboard the ground.
You accept affected the dispatch at which you kicked the brawl (in meters/second), the bend at which it launched, and how aerial you kicked it (in meters).
The aloft may complete like a agglomeration of algebraic gobbledygook. But it’s based on a actual simple, and actual important, abstraction from physics: you can amusement the vertical and accumbent motion of the brawl independently.
The absolute time spent in the air accumulated with how far forth the arena the brawl went tells you aggregate you charge to apperceive about the ball’s accumbent velocity. Ignoring air resistance, the brawl doesn’t acquaintance any accumbent acceleration, so its accumbent dispatch stays constant.
The ball’s vertical motion is a altered story. As anon it leaves your foot, force starts slowing the brawl down. Eventually, the ball’s vertical dispatch alcove zero. Afterwards that, the brawl turns about and starts falling aback to Earth, acrimonious up dispatch the absolute time. Ignoring air attrition (again!), the ball’s vertical dispatch aback it hits the arena is the aforementioned as its vertical dispatch aback you kicked it.
Since the final and antecedent vertical speeds are the same, we can focus on aloof the additional bisected of the ball’s trip. We can ask, how fast would a brawl be affective afterwards a assertive bulk of time if you alone it from a abundant height? That’s accession way of allurement how fast the brawl is traveling aback it hits the arena afterwards falling from the accomplished allotment of its journey. The “falling time” is bisected the adhere time.
The absolute dispatch comes from accumulation the accumbent and vertical velocities. We can draw the velocities like a adapted triangle. The accumbent and vertical velocities accomplish up the abandon of the triangle while the absolute dispatch is its hypotenuse. Application the Pythagorean Theorem, you can use the abandon to bulk out the absolute dispatch with which the brawl was launched. You can use the aforementioned triangle to bulk out the bend at which it took off.
Figuring out the acme comes aback to aloof annoying about the ball’s vertical motion. We apperceive how bound the brawl larboard your foot. And we apperceive how acerb force is alive to apathetic it down. That’s all we charge to bulk out how aerial the brawl went. It’s the aforementioned as alive how far your car will go if you’re active at 60mph and aback hit the brakes. Except, in this case, the brakes are gravity!
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