What is her maximum height off the ground ? How long after she leaves the trampoline does she reach the maxheight? How long is she in the air? How high is the trampoline off the ground?
A trampoline artist bounces on a trampoline. Her height above ground is modelled by the function `h=-4.9(t-1)^2+6.3` . h measures the height above the ground in metres , and t measures the time after she leaves the trampoline in seconds.
The given function is in vertex form of the parabola `y=a(x-k)^2+k` , where (h,k) is the vertex.
This indicates that the vertex of the function is (1, 6.3).
Since the sign of `a` in the function is negative, the vertex is the maximum point of the parabola.
Hence, the maximum height of the trampoline artist is 6.3m above the ground and it takes her 1 second to reach the maximum height.
To determine the amount of time that she is in the air, set the height above the ground equal to zero (h=0).
Set one side equal to zero.
Apply quadratic formula to solve for t.
`t=(-b+-sqrt(b^2-4ac))/(2a)=(-(-2)+-sqrt((-2)^2-4*1(-0.29)))/(2*1) = (2+-sqrt5.16)/2=(2+-2.27)/2`
`t = (2+2.27)/2=2.14` and `t=(2.-2.27)/2=-0.14`
Take only the positive value of t. This the amount of time the it takes the artist to reach the ground.
Hence, the artists is the air for 2.14 seconds.
Note that t measures the time after the artist leave the trampoline. So to determine the height of the trampoline above the ground, set t=0.
Thus, the trampoline is 1.4 meters above the ground.