In basketball, whenever anyone attempts a shot, its path can be predicted using a parabola, and its quadratic equation.
But what is a parabola?
parabola: Let l be a line and F be a point not on l. A parabola is the set consisting of every point in the plane of F and l
whose distance from F equals its distance from l.
A parabola can be represented by the quadratic equation. The quadratic equation, y = ax2 + bx + c , can be solved for x by using the quadratic formula: x = [-b ±sqrt(b2-4ac)] / 2a, "the quantity if -b plus or minus the square root of the quantity b2-4ac all divided by 2a". Obviously, to solve for y, just solve the right side of quadratic equation.
A basketball player shoots a basketball from his hand at an initial height of 1 m with an initial upward velocity of 10 meters per second. What is the equation to represent the height of the ball after 2 seconds?
1) First of all, we know that our equation must be in the form y=ax2+bx+c. Our equation is now h=rt2+vt+i, where h is the height after t seconds, r is 1/2 of the restraining force (gravity, in this case), v is the initial upward velocity, t is the number of seconds (time), and i is the initial height of the basketball.
2) Now that we have an equation, all that we have to do is substitute numeric values for the variables. h is what we have to find, so we leave it alone. r is 1/2 of gravity, which is -9.8 meters/second (it's negative because it drags down, while the shot is going up), so r is -4.9. t is time, which in this case is given in the problem as 2 seconds. v is the initial velocity, also given in the problem as 10 meters per second. Then, the last variable left is i, which is the initial height given in the problem as 1.
3) Now, our equation is h=-4.9*22+10*2+1. Then, we just solve the equation and our final answer is 1.4. So, the height of the ball after 2 seconds is 1.4 meters.
To give you a better familiarity with the quadratic equation, we have the equation solver below. Just enter your values and press the "solve" button.
Stumped? Take a look at the answer key!
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