Emily threw a hall up in the air from her tree house It foll

Emily threw a hall up in the air from her tree house It followed the path given by the parabola y = - 0.16x^2 + 7x +12. where x is the horizontal position of the ball (in feet from the tree house) and y is the vertical position of the ball (in feet above the ground). At what distance away from the tree house did the ball strike the ground?

Solution

The position of the ball is given by y = - 0.16x² + 7x + 12 where x is the horizontal distance from the tree house and y is the vertical distance from the ground. When the ball strikes the ground, y = 0. Therefore, - 0.16x² + 7x + 12 = 0 or. 0.16x² - 7x - 12 = 0 . On multiplying by 10, we have 16x² - 70x - 120 = 0. Therefore, x =   [ 70 ± { (-70)²– 4 (16)(-120)}] / 2*16 = { 70 ± ( 4900 + 7680)}/ 32 = ( 70 ± 12580)/ 32 =( 70 ± 112.1606)/ 32  or, x = (70 + 112.1606)/ 32 ( as x can not be negative) or, x = 182.1606/32 = 5.6925  or, x = 5 ft and 8.31 inches. Thus the distance of the ball from the tree house, when it falls to the ground, is 5 ft and 8.31inches

NOTE:

We know that the roots of the equation ax² + bx + c = 0 are [ - b ± ( b² - 4ac)] / 2a . This formula has been used.