If a rose thrown from a platform has a height, #h(t)#, given by the formula#h(t)= -16t^2 + 32t + 20#, how can you use the quadratic formula to determined how far it will travel before hitting ground?
The quadratic function
We now seek to determine at what time t will
This is equivalent to solving the quadratic equation
We may use the quadratic formula to solve this and obtain
But since time is scalar it cannot be negative so we discard the -0,5 value and conclude that
This means that the ball will be at height zero, ie the ground, exactly 2,5 seconds after being thrown.
We now still need to find what the maximum height reached by the stone is and to do that we differentiate the height function and set it to zero.
We can now evaluate the height function at the time when t = 1 second to find the distance above ground after the ascent to yield
Thus, the total distance travelled by the object is