The speed of the ball at which it should be thrown upward to reach a maximum height of .
The speed of the ball at which it should be thrown upward to reach a maximum height of is .
An object thrown or fired straight upward at an initial speed of ft/s will reach a height of h feet after t seconds, where h and t are related by the formula .
Discriminant of a quadratic equation:
The quantity is called the discriminant of a quadratic equation of the form , from which the number of solutions the quadratic equation can have, can be obtained.
1. If , there are two unequal real solutions.
2. If , there is a repeated real solution, a double root.
3. If , there is no real solution.
Substitute in and simplify the equation as .
Compare this equation with the general form .
Note that, the ball will reach the highest point only once and the quadratic equation has only one solution when the discriminant is zero.
Therefore, let the discriminant be zero.
On further simplifications, the following is obtained.
Since the speed should be always positive, the value of .
Thus, the speed of the ball at which it should be thrown upward to reach a maximum height of is .
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