Question

Alvin throws the football to a receiver who jumps up to catch the ball. The height of the ball over time can be represented by the quadratic equation -4.9t2 + 7.5t + 1.8 = 2.1 . This equation is based on the acceleration of gravity -4.9 m/s2, the velocity of his pass is 7.5 m/s and releases the football at a height of 1.8 meters, and the height where the receiver catches the ball of 2.1 meters. Put the equation in standard form and then solve by using the quadratic equation.

Answer 1

The standard form of the equation is 49t² - 75t + 3 = 0

The solution of the equations are 1.49 and 0.041

Explanation:

* Lets explain how to solve the problem

- The standard form of the quadratic equation is ax² + bx + c = 0,

where a , b , c are constant and a can not be 0

∵ The quadratic equation is -4.9t² + 7.5t + 1.8 = 2.1

- Lets make the left hand side equal to 0

∵ -4.9t² + 7.5t + 1.8 = 2.1 ⇒ subtract 2.1 from both sides

∴ -4.9t² + 7.5t - 0.3 = 0 ⇒ multiply each term by -10

∴ 49t² - 75t + 3 = 0

* The standard form of the equation is 49t² - 75t + 3 = 0

∵ ax² + bx + c = 0

∴ a = 49 , b = -75 , c = 3

- Lets use the formula
`x=\frac{-b+-\sqrt{b^(2)-4ac}}{2a}` to solve

the equation

∴
`x=\frac{-(-75)+\sqrt{(-75)^(2)-4(49)(3)}}{2(49)}=1.49`

∴
`x=\frac{-(-75)-\sqrt{(-75)^(2)-4(49)(3)}}{2(49)}=0.041`

* The solution of the equations are 1.49 and 0.041