HELP ON FIRST 3 PLS
1 answer:
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Given t = time and h = height
From the equation.
h is the axis od symmetry
(h, k) is the vertex.
In the equation, h is 1 and k is 16.
So the maximum value is 16 at t = 1.
The ball reaches maximum at 16 and it takes t = 1 to reach the maximum point.
Answer:
Step-by-step explanation:
The problem is very simple, since they give us the solution from the start. However I will show you how they came to that solution:
A differential equation of the form:
Will have a characteristic equation of the form:
Where solutions are the roots from which the general solution can be found.
For real roots the solution is given by:
For real repeated roots the solution is given by:
For complex roots the solution is given by:
Where:
Let's find the solution for using the previous information:
The characteristic equation is:
So, the roots are given by:
Therefore, the solution is:
As you can see, is the same solution provided by the problem.
Moving on, let's find the derivative of in order to find the constants
and
:
Evaluating the initial conditions:
And
Now we have found the value of the constants, the solution of the second-order IVP is:
Check the pictrue below.
