Answer:
Step-by-step explanation:
The motion of the dolphin is quadratic
i.e y=-16t²+20t
To get the maximum height the dolphin will reach
We need to find the point of inflexion. i.e dy/dt=0
dy/dt=-32t+20
Then set dy/dt=0
0=-32t+20
Then, -32t=-20
t=0.625
Let find d²y/dt²
d²y/dt²=-32. Since this is negative then the point t=0.625 is the maximum point the dolphin can reach
Then substitute t=0.625 into y
y=-16t²+20t
y=-16(0.625)²+20(0.625)
y=6.25ft
Then the maximum height the dolphin can reach is 6.25ft
Using discriminant
Formular method
y=-16t²+20t
So the dog height y<7
y=-16t²+20t <7
-16t²+20t-7<0
a=-16, b= 20. c=-7
t=(-b±√b²-4ac)/2a
Using the a, b and c direct for the discriminant
D=b²-4ac
D=20²-4×-16×-7
D=-48
Which is a complex number
Then the dolphin can reach the height
Then we need to model the D to be greater than 0
Therefore,
D>0
b²-4ac>0
We cannot do anything to a and b it is already given
a=-16, b=20
(20)²-4(-16c)>0
400+64c>0
64c>-400
Then
c>-6.25
Divide both side by - and the inequality sign will change
Therefore -c<6.25
So the dog height y<6.25
y=-16t²+20t <6.25
Therefore the maximum height is 6.25.
If it is greater than that then, we are going to have a complex root movement which is not possible for the dolphin .
