A projectile launcher upward with a velocity of 160 feet per second from the top of a 70-foot platform. What is the maximum heig
ht attained by the projectile?
1 answer:
Answer:
470 ft
Step-by-step explanation:
The equation for ballistic motion is usually written ...
h(t) = -16t^2 +v0·t +h0
where v0 is the initial upward velocity in ft/s, and h0 is the initial height in ft.
Filling in the numbers given in the problem statement, the equation becomes ...
h(t) = -16t^2 +160t +70
This can be rewritten to vertex form as follows.
h(t) = -16(t^2 -10t) +70
= -16(t^2 -10t +25) +70 +400 . . . . . . add and subtract 400 to complete the square
= -16(t -5)^2 +470
The vertex of the height vs. time curve is at (t, h) = (5, 470).
The maximum height attained is 470 feet.
You might be interested in
All integers where n ≥ 1.
We have given that the sequence,
We have to find the domain for n.
<h3>What is the meaning of arithmetic sequence?</h3>Arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. Difference here means the second minus the first.
That is,
where a = first term of sequence.
d =common difference.
n =number of terms which belongs to natural numbers
By the definition of arithmetic sequence n starts with 1
Remember that,the natural number starts with 1
Now, in given sequence for nth term
The domain for n is All integers where n ≥ 1.
To learn more about the arithmetic sequence visit:
You haven't provided the required roots, but I can tell you how to do this kind of exercises in general.
If the coefficient is 1, i.e. the equation is written like
, then you can say the following about the coefficients b and c:
is the opposite of the sum of the roots
is the multiplication of the roots.
So, for example, if we want an equation whose roots are 4 and -2, we have:
So, the equation is
If your roots are rational, you can work like this: suppose you want an equation with roots 3/4 and 1/2. You have:
And so the equation is
In order to have integer coefficients, you can multiply both sides of the equation by 8: