A projectile fired into the first quadrant from the origin of a coordinate system will pass through the point (x, y) at time t according to the relationship,
cos theta 2x/2y + gt2
where theta = the angle of elevation of the launcher and g = the acceleration due to gravity An artilleryman is firing at an enemy bunker located 2450 feet up the side of a hill that is 6175 feet away. He fires a round, and exactly 2.27 seconds later he scores a direct hit.
(a) What angle of elevation did he use?
(b) If the angle of elevation is also given by sec θ = υ0t/x. where υ0 is the muzzle velocity of the weapon, find the muzzle velocity of the artillery piece he used.

Answers

Answer 1

Answer:

a. 22.3°

b. 2940.16 ft/s

Step-by-step explanation:

Here is the complete question

A projectile fired into the first quadrant from the origin of a coordinate system will pass through the point (x, y) at the relationship cot theta = 2x/2y + gt^2 where theta is the angle of elevation of the launcher and g is the acceleration due to gravity (32.2 feet/second^2). An artillery man is firing at an enemy barker located 2275 feet up the side of a hill that is 6325 feet away. He fires a round, and exactly 2.84 seconds later he scores a direct hit.

a. What angle of elevation did he use? theta = degree (Do not round until the final answer. Then round to one decimal place as needed.)

b. f the angle of elevation is also given by sec theta = v_0 t/x, where v_0 is the velocity of the weapon, find the muzzle velocity of the artillery piece he used. v_0 = feet/second (Round to two decimal places as needed.)

Solution

(a) What angle of elevation did he use?

Given that cosθ = 2x/(2y + gt²) where x = horizontal distance of projectile = 6175 feet away,y = vertical distance of projectile = 2450 feet up, g = acceleration due to gravity = 32 ft/s² and t = time of hit = 2.27 s

So, cosθ = 2x/(2y + gt²)

cotθ = 2 × 6175 ft/(2 × 2450 ft + 32 ft/s² × (2.27 s)²)

cotθ = 12350 ft/(4900 ft + 32 ft/s² × 5.1529 s²)

cotθ = 12350 ft/(4900 ft + 164.8928 ft)

cotθ = 12350 ft/(5064.8928 ft)

1/tanθ = 2.4384

tanθ = 1/2.4384

tanθ = 0.4101

θ = tan⁻¹(0.4101)

θ = 22.3°

(b) If the angle of elevation is also given by sec θ = υ0t/x. where υ0 is the muzzle velocity of the weapon, find the muzzle velocity of the artillery piece he used.

Making u0 subject of the formula, we have

u0 = xsecθ/t

u0 = x/tcosθ

since x = 6175ft, t = 2.27 s and θ = 22.3°, then

u0 = x/tcosθ

u0 = 6175 ft/(2.27 s × cos22.3°)

u0 = 6175 ft/(2.27 s × 0.9252)

u0 = 6175 ft/(2.1 s)

u0 = 2940.16 ft/s


Related Questions

Simplify
1/6 / 1 3/8

Answers

Answer:

1/6 = 1/6 (already simplified) 1 3/8 = 11/8

Step-by-step explanation:

jane bought 5 3/5 boxes of raspberries and 2 1/4 boxes of strawberries. How much more boxes of raspberries did jane buy?

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Answer: 3 7/20

Step-by-step explanation:

5 3/5 - 2 1/4

Find GCD.

5 12/20 - 2 5/20

3 7/20 more boxes of raspberries than strawberries

tam
If ABCD is dilated by a factor of 2, the
coordinate of A' would be:
5
4
3
С
2
B
1
-8 -7 -6
-5
-3-2
-10
1
2
3
5
6
7
8
9 10
А
-2
D
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A' = ([?], [D

Answers

Answer:

-6,-2 is the answer!!

Step-by-step explanation:

The coordinate of A' would be (-6, -2)

Dilation of figure

Dilation is a transformation technique that changes the size of an object by a scale factor "k"

From the diagram shown, the measure of the coordinate point is given as (-3, -1).

If the coordinate A is dilated by a factor of 2, the resulting coordinate A' will be given as:

A' = (2(-3), 2(-1)) = (-6, -2)

Hence the  coordinate of A' would be (-6, -2)

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Work out the mean for the data set below: 5, 6 Give your answer as a decimal.

Answers

Answer:

5.5

Step-by-step explanation:

5 + 6 =

11 / 2 =

5.5

Use the Law of Cosines to find the measure of ∠F. Round to the nearest degree.
f = 5, g = 6, h = 7

Use: f² = g² + h² – 2gh cos F

Answers

Answer:

Solution given.

f = 5, g = 6, h = 7

<F=?

we have;

f² = g² + h² – 2gh cos F

5²-6²-7²=-2×6×7 cos F

-60/-84=cos F

F=cos-¹(5/7)=44.41°

<F=44.4° is a required answer

Can someone higher please help ?

Answers

.....................................................................................

Answer: -0.833 (repeating decimal)

Step-by-step explanation: fg(x) means plug the g(x) equation into f(x), and for gf(x) it’s vice versa:

Fg(x) = 3x^2 - 1 + 2

Gf(x) = 3(x + 2)^2 - 1

First, we should simplify gf(x) to eliminate the (x + 2)^2:

3(x^2 + 4x + 4) - 1

3x^2 + 12x + 12 - 1

3x^2 + 12x + 11

Second, simplify fg(x) by solving -1 + 2: 1

Now, we can set the two equations equal to each other and solve:

3x^2 + 1 = 3x^2 + 12x + 11 (subtract 3x^2 from each other and 1 from 11)

-10 = 12x (Divide)

-0.8333... = x

To make sure this answer is correct, plug -0.833 into the original equations and set them equal to each other:

3(-0.833)^2 + 1 = 3(-0.833)^2 + 12(-0.833] + 11

3.083 = 3.083

Which of these tables represents a function?
Table A
Table B
Table C
Table D

Answers

Table B
Hope this help

56,252 rounded to the nearst ten thousandths

Answers

Answer:

60,000

Step-by-step explanation:

Answer:

60,000

Step-by-step explanation:

The number of members in a labor union is 240, and the number increases by 5% each year. Find the number of members after 4 years.​

Answers

Answer: 292

Step-by-step explanation:

Given

There are 240 members in a labor union

The number increases by 5% each year

After 1 year it is

[tex]\Rightarrow 240+5\%\times 240\\\Rightarrow 240(1+0.05)[/tex]

After 2 years

[tex]\Rightarrow 240(1+0.05)+5\%\times 240(1+0.05)\\\Rightarrow 240(1+0.05)(1+0.05)=240(1+0.05)^2[/tex]

Similarly, after 4 years

[tex]\Rightarrow 240(1+0.05)^4\\\Rightarrow 291.72\approx 292[/tex]

observa con atencion los siguientes desarrollos planos y encierra con cual de ellos se puede armar cada cuerpo uno de ellos tiene dos respuestas

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Answer:

Can you give it in a english

Step-by-step explanation:

Determine whether each ordered pair is a solution of the inequality-3x-4y<6

Answers

Answer:

it's (6,0) I can't explain though

Simplify (-32) divided by (-4)

Answers

Answer:

[tex] \frac{8}{1} [/tex]

Step-by-step explanation:

[tex] \frac{ - 32}{ - 4} [/tex]

Reduce factor by 4

[tex] \frac{ - 8}{ - 1} [/tex]

A negative divided by a negative equal positve so

[tex] \frac{8}{1} [/tex]

the simplest form of 32/4 is 8/1

find the GCD ( or HCF) of numerator and denominator GCD of 32 4 is 4

divide both the numerator and denominator GCD

32/4 ÷ 4/4

reduce fraction: 8/1

therefore, 32/4 simplify to lowest terms is 8/1.

What is the line segment from the center of the circle to any point on the circle



please help me Answer this question​

Answers

Step-by-step explanation:

the circle to any point on the circle

Answer:

Radius

.....................

In ΔMNO, the measure of ∠O=90°, OM = 69 feet, and NO = 16 feet. Find the measure of ∠N to the nearest tenth of a degree.

Answers

9514 1404 393

Answer:

  76.9°

Step-by-step explanation:

The relevant trig relation is ...

  Tan = Opposite/Adjacent

  tan(N) = OM/ON

  N = arctan(OM/ON) = arctan(69/16)

  N ≈ 76.9°

HELP! PLEASEEEEE
IMAGE BELOW!

Answers

Answer:

Quadrant I and Quadrant II

Step-by-step explanation:

Quadrant I has both positive x and y coordinates,Quadrant II has a negative x coordinate but the y coordinate is positive.

Quadrant one and quadrant two lmk if this helps

5 times the sum of 24 and 7

Answers

Answer:

Your answer should be 155!

Step-by-step explanation:

Sum means to add, so 24 + 7 = 31

31 x 5 = 155

I hope this helps!

A summation, also called a sum, is the result of arithmetically adding numbers or quantities. 155 is the answer for 5 times the sum of 24 and 7.

What is Sum?

A summation, also called a sum, is the result of arithmetically adding numbers or quantities.

Given,

5 times the sum of 24 and 7

Sum is nothing but addition.

When we see the word sum it means we are adding some value with other factor. In the given problem 24 and 7 are added.

Times means multiplication.

We have to convert 5 times the sum of 24 and 7 to expression.

When we see times, it means product or we are multiplying a number with the other number. Here with 5 we are multiplying the sum of 24 and 7.

5×(24+7)

Firstly we calculate value in parenthesis.

twenty four plus seven is thirty one.

5×31

The product of 5 and 31 is 155.

155

Hence 155 is the answer for 5 times the sum of 24 and 7.

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What is the end behavior of this radical? f(x) = 4 square root x - 6

Answers

Answer:

I think you can answer it with a chart, I guess, of course I'm not sure‍♀️

if a1= 7 and r=3, find a4

Answers

Answer:

a4 = 189

Step-by-step explanation:

Geometric sequence:

In a geometric sequence, the quotient r between consecutive terms is always the same.

The nth term of the sequence is given by:

[tex]a_n = a_1*r^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term.

In this question:

[tex]a_1 = 7, r = 3[/tex]

The fourth term is:

[tex]a_4 = 7*3^3 = 189[/tex]

So

a4 = 189

vTo estimate the parameter stated in question 2, the following was done. A simple random sample of 22 students who attended a review session was selected, and the mean grade on test 7 for this sample of 22 students was 85 with a standard deviation of 9.8. An independent simple random sample of 47 students who did not attend a review session was selected, and the mean grade on test 7 was 77 with a standard deviation of 10.6. If appropriate, use this information to calculate and interpret a 90% confidence interval for the difference in the mean grade on test 7 for all students who attended a review session and for all students who did not attend a review session.

Answers

Answer:

The 90% confidence interval for the difference in the mean grade on test 7 for all students who attended a review session and for all students who did not attend a review session is (3.7, 12.3).

Step-by-step explanation:

Before building the confidence interval, we need to understand the central limit theorem and subtraction between normal variables.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

A simple random sample of 22 students who attended a review session was selected, and the mean grade on test 7 for this sample of 22 students was 85 with a standard deviation of 9.8.

This means that:

[tex]\mu_A = 85, s_A = \frac{9.8}{\sqrt{22}} = 2.09[/tex]

An independent simple random sample of 47 students who did not attend a review session was selected, and the mean grade on test 7 was 77 with a standard deviation of 10.6.

This means that:

[tex]\mu_N = 77, s_N = \frac{10.6}{\sqrt{47}} = 1.55[/tex]

Distribution of the difference in the mean grade on test 7 for all students who attended a review session and for all students who did not attend a review session.

Mean:

[tex]\mu = \mu_A - \mu_N = 85 - 77 = 8[/tex]

Standard deviation:

[tex]s = \sqrt{s_A^2 + s_B^2} = \sqrt{2.09^2 + 1.55^2} = 2.6[/tex]

Confidence interval:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.9}{2} = 0.05[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.05 = 0.95[/tex], so Z = 1.645.

Now, find the margin of error M as such

[tex]M = zs[/tex]

So

[tex]M = 1.645*2.6 = 4.3[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 8 - 4.3 = 3.7

The upper end of the interval is the sample mean added to M. So it is 8 + 4.3 = 12.3

The 90% confidence interval for the difference in the mean grade on test 7 for all students who attended a review session and for all students who did not attend a review session is (3.7, 12.3).

Choose the Inequality that matches the graph below.

Answers

Answer:

The answer would be A

Step-by-step explanation:

Because the circle is an open circle, also its point towards the positive so that means A is the correct answer

if a line passing through (4,-p) and (-2,6)is parallel to 2y+3x= -3, find p.​

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Answer:

Step-by-step explanation:

Can someone solve these for me?

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Answer:

In order of pictures,

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Picture #2: 140

Picture #3: 9.9

Picture #4: 13.5

Picture #5: 7.07

Step-by-step explanation:

I am not entirely sure that 3 - 5 are correct, but I know that 1 and 2 are correct. I am sorry if they are incorrect.

Hope that this helps!

Jill Kingman pays a $419.00 premium annually. This represents 35% of the total premium. The rest of the premium is paid by her employer.

Use a thousands comma where applicable.

1. the company's percentage
%
2. the total premium $
3. the company's payment $

Answers

1. 100 - 35 = 65% company percent
2. 419/.35 = 1197 total premium
3. .65 *1197 = 778.05 company payment

Calculate the missing values.

Jill Kingman pays a $419.00 premium annually. This represents 35% of the total premium. The rest of the premium is paid by her employer.

Use a thousands comma where applicable.

1. 100 (100% of cost)  - 35 = 65% company percent

2. 419.00 ÷ .35 (or, 35%, but use the decimal) = 1197 total premium

3. 0.65 × 1197 = 778.05 company payment

I tried to make it so you could see where the numbers came from, by making the ones bold, others, italics, and other combinations. I hope you understand what I did. I tried to explain how the guy above did it. He did well, so brainliest goes to him.

A box contains 4 yellow markers, 3 blue markers, 6 black markers and 2 red markers. Suppose a marker is chosen randomly, and then returned to the box.
Determine the probability of selecting a yellow marker, then a red marker.

Answers

Answer:

4+3+6+2 = 15

Step-by-step explanation:

selecting a yellow marker 4/15

selecting a red marker 2/15

which table represents a linear function? HELP FAST PLEASE

Answers

Answer:

the bottom left

Step-by-step explanation:

A linear function will have a constant slope so the bottom left graph is the only one with a constant slope. The y-values are all increasing by 2.

Help me please? I’ll give out brainly. No links.

Answers

Answer:

A = 8 unites

Step-by-step explanation:

8 - 2 = 6

the y-intercept stays the same

only x-intercept changes

Answer:sorrY mAaM cAnt heLp yOu

Step-by-step explanation:

1/10 *as a fraction* divided by 5
Please help! Fast!!​

Answers

Answer:

1/50

Step-by-step explanation:

1/10÷5/1=

1/10•1/5=

1/50

An equation of the line through the points (-2.5) and (3, -4) is:​

Answers

linear??? . z z z z z z z z

This dot plot is not symmetric, and the data set has two
extreme values.
.
2
3
8
What is the best measure of center for this dot plot?
O A. The mean absolute deviation (MAD)
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D. The mean

Answers

the answer would be b

Answer:

C: The median

Step-by-step explanation:

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