SOLUTION: A ball is thrown vertically upwards from the top of a school building. It’s height, h metres, above the ground, can be modelled by h=18+6t-4t^2, where t is the time in seconds afte

The correct equation written for the Earth conditions, must have coefficient EITHER -4.9 at t^2,  OR -5,


depending on which value of the gravity acceleration,  9.81 m/s^2   or simply rounded 10 m/s^2 is used.


Simply speaking,  your equation is written incorrectly,


so further discussion makes no sense.

    You may often meet these problems on a projectile thrown vertically upward.

    The equation for the height over the ground usually has ONE OF TWO POSSIBLE forms:

        a)  h(t) = -16*t^2 + v*t + c

                 In this form, the equation is written for the height h(t) over the ground measured in feet.
                 The value of "16" is the half of the value of the gravity acceleration g = 32 ft/s^2.

                 The sign "-" at the first term means that the gravity acceleration is directed down, 
                 while the "y"-axis of the coordinate system is directed vertically up, in the opposite direction.

                 The value of "v" in this equation is the value of the initial vertical velocity. 

                 The value of "c" is the initial height over the ground.

                 The ground level is assumed to be 0 (zero, ZERO). In other words, the origin of the coordinate system is at the ground.


        b)  h(t) = -5*t^2 + v*t + c

                 It is another form of the "height" equation for the same process.

                 In this form, the height h(t) is measured in meters (instead of feet).

                 The value of "5" at the first term is the same gravity acceleration, but this time expressed in "m/s^2" units" g = 10 m/s^2.

                       Actually, more precise value is g = 9.8 m/s^2, therefore, sometimes, this equation goes with the first term -4.9.

                 The value of "v" is the vertical velocity, expressed in m/s.

                 The value of "c" is the initial height over the ground in meters.