If the measure of ZDEF is 65°, what is the measure of DE?

A small rocket is fired from a launch pad 10 m above the ground with an initial velocity left angle 250 comma 450 comma 500 righ

jonny [76]

Let $\vec r(t),\vec v(t),\vec a(t)$ denote the rocket's position, velocity, and acceleration vectors at time $t$ .

We're given its initial position

$\vec r(0)=\langle0,0,10\rangle\,\mathrm m$

and velocity

$\vec v(0)=\langle250,450,500\rangle\dfrac{\rm m}{\rm s}$

Immediately after launch, the rocket is subject to gravity, so its acceleration is

$\vec a(t)=\langle0,2.5,-g\rangle\dfrac{\rm m}{\mathrm s^2}$

where $g=9.8\frac{\rm m}{\mathrm s^2}$ .

a. We can obtain the velocity and position vectors by respectively integrating the acceleration and velocity functions. By the fundamental theorem of calculus,

$\vec v(t)=\left(\vec v(0)+\displaystyle\int_0^t\vec a(u)\,\mathrm du\right)\dfrac{\rm m}{\rm s}$

$\vec v(t)=\left(\langle250,450,500\rangle+\langle0,2.5u,-gu\rangle\bigg|_0^t\right)\dfrac{\rm m}{\rm s}$

(the integral of 0 is a constant, but it ultimately doesn't matter in this case)

$\boxed{\vec v(t)=\langle250,450+2.5t,500-gt\rangle\dfrac{\rm m}{\rm s}}$

and

$\vec r(t)=\left(\vec r(0)+\displaystyle\int_0^t\vec v(u)\,\mathrm du\right)\,\rm m$

$\vec r(t)=\left(\langle0,0,10\rangle+\left\langle250u,450u+1.25u^2,500u-\dfrac g2u^2\right\rangle\bigg|_0^t\right)\,\rm m$

$\boxed{\vec r(t)=\left\langle250t,450t+1.25t^2,10+500t-\dfrac g2t^2\right\rangle\,\rm m}$

b. The rocket stays in the air for as long as it takes until $z=0$ , where $z$ is the $z$ -component of the position vector.

$10+500t-\dfrac g2t^2=0\implies t\approx102\,\rm s$

The range of the rocket is the distance between the rocket's final position and the origin (0, 0, 0):

$\boxed{\|\vec r(102\,\mathrm s)\|\approx64,233\,\rm m}$

c. The rocket reaches its maximum height when its vertical velocity (the $z$ -component) is 0, at which point we have

$-\left(500\dfrac{\rm m}{\rm s}\right)^2=-2g(z_{\rm max}-10\,\mathrm m)$

$\implies\boxed{z_{\rm max}=125,010\,\rm m}$

7 0

2 years ago

Find the least common multiple of 5 10 and 15

Sedbober [7]

The answer to the question

7 0

3 years ago

Harry and Larry are having a barbecue dinner. The probability of Harry staining his shirt during the dinner is

Anettt [7]

Answer:

A

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

The average salary for a construction worker is $29,160 per year. A veterinarian makes on average $84,460. If you consider the e

wel

Hey !

I am going to explain what I did to get the answer...

I multiplied $29,160 by 30 = $874,800
Then I multiplied $84,460 by 30 = $2,533,800

Then I subtracted the results = a difference of $1,659,000

So the answer to your question is, $1,659,000 is the difference.

I hope I was able to help you out :D <span />

5 0

3 years ago

Read 2 more answers

The graph below shows a company’s profit f(x), in dollars, depending on the price of the erasers x, in dollars, being sold by th

Alex777 [14]

The x-intercept = (0, 0) and (8, 0), Rate of function is 50 and as the price of erasers increasing the company's profit increasing and when price of the eraser decreasing the price the company's profit decreasing.

<h3>What is a function?</h3>

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a graph of a function:

From the graph:

x-intercept = (0, 0) and (8, 0)

Maximum value of the graph = 270 at x = 4

Increasing in the interval x ∈ (0, 4)

Decreasing in the interval x ∈ (4, 8)

As the price of erasers increasing the company's profit increasing and when price of the eraser decreasing the price the company's profit decreasing.

Rate of function = (270-120)/(4-1) = 50

Thus, the x-intercept = (0, 0) and (8, 0), Rate of function is 50 and as the price of erasers increasing the company's profit increasing and when price of the eraser decreasing the price the company's profit decreasing.

Learn more about the function here:

brainly.com/question/5245372

#SPJ1

8 0

2 years ago