Use the method of undetermined coefficients to find one solution of y''-10y'+26y=9e^6t
1 answer:
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A) 436 ft
B) t = 5 sec
C) 5.60 s
Step-by-step explanation:
A)
The height of the ball at time t is given by the equation
where
is the acceleration of the ball (acceleration of gravity, downward)
+500 is the initial height of the ball, at time t = 0
Here we want to find the height of the ball after 2 seconds, so at a time of
t = 2 s
Substituting into the equation, we find:
B)
Here we want to find the time it takes for the ball to fall to a height of 100 feet above the ground, so the time t at which
h(t) = 100 ft
As stated in the text of the question, the height of the ball at time t is given by
Since
h(t) = 100, we have
And solving for t we find:
So, the correct solution is the positive one:
t = 5 sec
C)
The ball reaches the ground when the height of the ball has became zero:
The height of the ball at time t is given by
And substituting
h(t) = 0
We get
And solving the equation for t, we find the time t at which the ball reaches the ground:
So, the correct solution is the positive one:
t = 5.60 s