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3 years ago

How would I do this?

Mathematics

1 answer:

Georgia [21]3 years ago

3 0

Work shown above! Answer would be 110 degrees!

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On an alien planet with no atmosphere, acceleration due to gravity is given by g = 12m/s^2. A cannonball is launched from the or

almond37 [142]

Answer:

a) $\vec r (t) = \left[(90\cdot \cos \theta)\cdot t \right]\cdot i + \left[(90\cdot \sin \theta)\cdot t -6\cdot t^{2} \right]\cdot j$ , b) $\theta = \frac{\pi}{4}$ , c) $y_{max} = 84.375\,m$ , $t = 3.75\,s$ .

Step-by-step explanation:

a) The function in terms of time and the inital angle measured from the horizontal is:

$\vec r (t) = [(v_{o}\cdot \cos \theta)\cdot t]\cdot i + \left[(v_{o}\cdot \sin \theta)\cdot t -\frac{1}{2}\cdot g \cdot t^{2} \right]\cdot j$

The particular expression for the cannonball is:

$\vec r (t) = \left[(90\cdot \cos \theta)\cdot t \right]\cdot i + \left[(90\cdot \sin \theta)\cdot t -6\cdot t^{2} \right]\cdot j$

b) The components of the position of the cannonball before hitting the ground is:

$x = (90\cdot \cos \theta)\cdot t$

$0 = 90\cdot \sin \theta - 6\cdot t$

After a quick substitution and some algebraic and trigonometric handling, the following expression is found:

$0 = 90\cdot \sin \theta - 6\cdot \left(\frac{x}{90\cdot \cos \theta} \right)$

$0 = 8100\cdot \sin \theta \cdot \cos \theta - 6\cdot x$

$0 = 4050\cdot \sin 2\theta - 6\cdot x$

$6\cdot x = 4050\cdot \sin 2\theta$

$x = 675\cdot \sin 2\theta$

The angle for a maximum horizontal distance is determined by deriving the function, equalizing the resulting formula to zero and finding the angle:

$\frac{dx}{d\theta} = 1350\cdot \cos 2\theta$

$1350\cdot \cos 2\theta = 0$

$\cos 2\theta = 0$

$2\theta = \frac{\pi}{2}$

$\theta = \frac{\pi}{4}$

Now, it is required to demonstrate that critical point leads to a maximum. The second derivative is:

$\frac{d^{2}x}{d\theta^{2}} = -2700\cdot \sin 2\theta$

$\frac{d^{2}x}{d\theta^{2}} = -2700$

Which demonstrates the existence of the maximum associated with the critical point found before.

c) The equation for the vertical component of position is:

$y = 45\cdot t - 6\cdot t^{2}$

The maximum height can be found by deriving the previous expression, which is equalized to zero and critical values are found afterwards:

$\frac{dy}{dt} = 45 - 12\cdot t$

$45-12\cdot t = 0$

$t = \frac{45}{12}$

$t = 3.75\,s$

Now, the second derivative is used to check if such solution leads to a maximum:

$\frac{d^{2}y}{dt^{2}} = -12$

Which demonstrates the assumption.

The maximum height reached by the cannonball is:

$y_{max} = 45\cdot (3.75\,s)-6\cdot (3.75\,s)^{2}$

$y_{max} = 84.375\,m$

7 0

3 years ago

In a large county in Central Pennsylvania, 42% of all registered voters are Democrats and 53% are Republicans. What is the proba

AVprozaik [17]

Answer:

Probability [Randomly selected voter affiliated with other party] = 1/20

Step-by-step explanation:

Given:

Percentage of Democrats voters = 42%

Percentage of Republican voters = 53%

Find:

Probability [Randomly selected voter affiliated with other party]

Computation:

Percentage of other party voters = 100% - [Percentage of Democrats voters + Percentage of Republican voters]

Percentage of other party voters = 100% - [42% + 53%]

Percentage of other party voters = 100% - 95%

Percentage of other party voters = 5%

Probability [Randomly selected voter affiliated with other party] = Percentage of other party voters / 100%

Probability [Randomly selected voter affiliated with other party] = 5% / 100%

Probability [Randomly selected voter affiliated with other party] = 1/20

8 0

2 years ago

In a diving meet, you score 8.4 and 7.88.<br><br> What is your total score?

JulijaS [17]

Answer: 16.28?

Step-by-step explanation:

4 0

2 years ago

2. David determines that 3 sqrt 2 cis(7pi/4) = -3+3i. When he considers the graphical representation of these numbers, he knows

fiasKO [112]

The correct rectangular equivalence of 3sqrt(2)·cis(7pi/4 ) is:

3sqrt(2)·cos( 7pi/4 ) + i·sqrt(2)·sin( 7pi/4 ) = 3 - 3i.

<h3>Where did David go wrong?</h3>

David mistakenly interchanged the Sin function and the Cos function when he was calculating the problem.

Hence the correct rectangular equivalence is:

3sqrt(2)·cos( 7pi/4 ) + i·sqrt(2)·sin( 7pi/4 ) = 3 - 3i.

<h3>What is rectangular equivalence?</h3>

An equation is rectangular in form when it is comprised of Variables like X and Y and can be represented on a Cartesian Plane.

Learn more about rectangular equivalence at:
brainly.com/question/27813225
#SPJ1

5 0

1 year ago

Which integer is closest to 0 on the number line?

IrinaVladis [17]

An integer is close to zero if it is "small".

By small, we mean that it is small in absolute value. In fact, for any given distance $d$ , there are two integers that are $d$ units away from zero: $d$ and $-d$ .

So, for example, -6 is close to zero than 8, because -6 is six units away from zero, while 8 is eight units away from zero.

So, the answer is B, -8, because it is 8 units away from zero. The other options A, C and D are, respectively, 12, 10 and 14 units away from zero.

8 0

2 years ago