the initial vertical velocity of a rocket shot straight up is 42 meters per second. How long does it take for the rocket to return to earth? round your answer to the nearest tenth of a second. show all your work.

Answers

Answer 1

It takes 4.3 seconds for the rocket to return to earth.

The equation is:
[tex]0=-9.8t^2+v_0t+h_0[/tex]
where -9.8m/sec² is the acceleration due to gravity, v₀ is the initial velocity, and h₀ is the initial height. We will go from the assumption that the rocket is launched from the ground, so h₀=0, and we are told that the initial velocity, v₀, is 42. This gives us:

[tex]0=-9.8t^2+42t[/tex]

We will use the quadratic formula to solve this. The quadratic formula is:
[tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

Plugging in our information we have:
[tex]t=\frac{-42\pm \sqrt{42^2-4(-9.8)(0)}}{2(-9.8)} \\ \\=\frac{-42\pm \sqrt{1764-0}}{-19.6} \\ \\=\frac{-42\pm \sqrt{1764}}{-19.6} \\ \\=\frac{-42\pm 42}{-19.6}=\frac{-42-42}{-19.6} \text{ or } \frac{-42+42}{-19.6} \\ \\=\frac{-84}{-19.6}\text{ or }\frac{0}{-19.6} \\ \\=4.3\text{ or }0[/tex]

x=0 is when the rocket is launched; x=4.3 is when the rocket lands.

Answer 2

Final answer:

The rocket takes approximately 8.6 seconds to return to earth.

Explanation:

To calculate the time it takes for the rocket to return to earth, we need to consider the projectile motion in the vertical direction. The initial vertical velocity of the rocket is 42 m/s. We can use the equation for vertical displacement to find the time:

Δy = v0yt + (1/2)gt²

Since the rocket returns to the same altitude, the displacement is 0. Therefore, we have:

0 = (42)t + (1/2)(-9.8)t²

Simplifying this equation and solving for t, we find that it takes approximately 8.6 seconds for the rocket to return to earth.

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Related Questions

are the expressions 3(y+1) and 3y+3 equivalent for any value of y? explain.

Answers

Yes they are the same hope I helped

brainliest pts pls

A swimming pool is Mark down to 695 from 1225,what is the percent markdown?

Answers

Aloha!
The percentage markdown from 1225 to 695 is: 56.78%
So, the swimming pool has a 56.78% markdown.

Adios! :)

[tex]\text {Markdown = } 1225 - 695 = 530[/tex]

[tex]\text {Percentage Markdown = } \dfrac{530}{1225} \times 100[/tex]

[tex]\text {Percentage Markdown = } \dfrac{53000}{1225} [/tex]

[tex]\text {Percentage Markdown = } 43.27 \ \% \text { (nearest hundredth)}[/tex]

7 yd 2 ft = How many feet ?

Answers

1 yard = 3 feet

7 yard = 21 feet

21 + 2 = 23 feet

3*7+2= 23 feet is your answer

What are the amounts of interest and maturity value of a loan for 150,000 at 6 1/2% simple interest for 3 years?

Answers

The formula for computing the amount of simple interest is:

I = Prt

Where P = principal amount of the loan

r = interest rate of the loan

t = duration of the loan

Substituting the amounts in the formula,

I = (150,000) (6.5%) (3)

= 29,250

To compute for the maturity value, you have to add the interest to the principal amount:

Maturity value = 150,000 + 29,250 = 179,250

Final answer:

To calculate the amount of interest and maturity value of a loan, use the formula: Interest = Principal × Rate × Time. In this case, the interest is $29,250 and the maturity value is $179,250.

Explanation:

To calculate the amount of interest and maturity value of a loan, we can use the formula:

Interest = Principal × Rate × Time

Maturity Value = Principal + Interest

In this case, the principal is $150,000, the rate is 6.5% (0.065 in decimal form), and the time is 3 years.

Step 1: Calculate the interest

Interest = $150,000 × 0.065 × 3 = $29,250

Step 2: Calculate the maturity value

Maturity Value = $150,000 + $29,250 = $179,250

Therefore, the amount of interest is $29,250 and the maturity value of the loan is $179,250.

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The equation - 5x² + 72x + 378 models the number of students enrolled in a school where x is the number of years since the school first opened in 1990. Which statement is true? A - Enrollment exceeded 650 students at one point B Enrollment never exceeded 650 students C The highest enrollment of any year was exactly 650 students D There were two years where 650 students were enrolled

Answers

i think the answer is a

c/9 - 8 = 17
Solve the equation and show all work please show steps!!

Answers

C/9 - 8 = 17
------------
Simplify
1/9c - 8 = 17
----------------
Add 8 to each side
1/9c - 8 + 8 = 17 + 8
1/9c = 25
--------------------
Multiply each side by 9
9 * 1/9c = 9 * 25
c = 225

Figure ABCD is a parallelogram.
What is the value of x?

Answers

X=7 because the side with the equation is the same length as the side that’s 38, so you just subtract 3 from 38 and then divide 35 by 5. You get 7. So, x=7

Hope this helps:)
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Hey there :)

A parallelogram is a quadrilateral which has 2 parallel sides

We can conclude that
AD = BC
5x + 3 = 38
Subtract 3
5x = 38 - 3
5x = 35
Divide by 5 to isolate x
[tex] \frac{5x}{5} = \frac{35}{5} [/tex]
x = 7

there are 33 seventh graders and 27 eighth graders in band, and 9 members of the band play trumpet. What decimal describes the portion of band members that play trumpet?

Answers

33+27=60. 9/60= .15 there's not much more to say.

Can someone please help

Answers

x= # tickets Shaun sold
1/2x+3= # tickets Trudy sold

Add them together.

= x + (1/2x + 3)
combine like terms
= (x + 1/2x) + 3
= 1 1/2x + 3
convert to improper fraction
= 3/2x + 3

ANSWER: 3/2x + 3 (3rd choice down)

Hope this helps! :)

Howard planted a tree in his front yard six months, one week, and two days ago. If today is August 13th, what day did Howard plant the tree in his yard?

A. February 4
B. February 13
C. February 20
D. February 22

Answers

For this to be easier, we know the date is February, since we are subtracting the 6 months. So let's start with February 13th, and subtract a week. One week is equal to 7 days, so 13-7= 6. We're now on February 6th, and we still have to subtract 2 days. 6-2=4, so we are at our date. A, Howard planted a tree in his front yard on February 4th.

Answer: February 4

Step-by-step explanation:

factory A has printed 700 books and Prints 50 new books every week. Factory has printed 300 books and prints 100 books every week. How many weeks will it be before a factory B has printed as many books as Factory A?

Answers

8 weeks. By that time both factories will have printed 1,100 books
Hope this helps

700 - 300 = 400
400/ 100 = 4
4 x 50 = 200
200/ 100 = 2

2+4= 6
6 weeks

Which formula can be used to describe the sequence? , −4, −24, −144,...

Answers

-4 to -24 you have to multiply 6

-24 x 6 = -144

Formula

a(n) = -4x6(n-1)

Answer:

[tex]An= -4(6)^{n-1}[/tex]

Step-by-step explanation:

−4, −24, −144,...

There is no common difference

-24/-4= 6

-144/ -24= 6

common ratio = 6

when there is a common ratio then it is an Geometric sequence

[tex]An= a1(r)^{n-1}[/tex]

a1 is the first term = -4

r is the common ratio = 6

Formula becomes

[tex]An= -4(6)^{n-1}[/tex]

List all the angles which are congruent to angle A!! ( a pair of parallel lines is cut by a transversal as shown in the figure)

Answers

Answer: A, C, E, & G

Step-by-step explanation:

can you tell me the solution to -3 (p + 1) equal to -18

Answers

-3p-3=-18
-3p=-18+3
-3p=-15
p=5

Hi there!

The answer to the inequality given is p ≥ 5

To get there follow these steps:
1. Distribute the -3, -3p-3≤-18
2. Add -3 to both sides, {-3p (-3 + 3 = 0) ≤ (-18 + 3 = -15)} = -3p ≤ -15
3. Divide both sides by -3, [tex] \frac{-3p}{-3} [/tex] ≤ [tex] \frac{-15}{-3} [/tex]
4. The final answer is p ≥ 5

If you need this graphed see below:

-ASIAX Frequent Answerer

A recipe for fruit punch uses 3 cups of apple juice for every 2 cups of grape juice. The table and graph show how many cups of each to use for different batch sizes. How many cups of grape juice do you need to make a batch that contains 12 cups of apple juice?

Answers

So... first you see that you have 12 cups of apple juice. Just do 12 divided by 3 and you'll get 4. Then break the 4 into ones and for every one you'll have two cups of grape juice. So.... 4 batches of punch will require 8 cups of grape juice.

Carrie is buying bulk candy for a high school fundraiser. She buys 1000 candy bars for $350. What is the unit cost per candy bar?
A) $.30
B) $.35
C) $.45
D) $1.35

Answers

Turn this problem into a fraction.
350/1,000 = 0.35

The answer is B - $.35

B). $.35

Unit cost = total cost / total no. of units
= $350 / 1000
= $.35

Find the missing number(?) so that the equation has no solutions. ?x+3=3(-x+7)

Answers

I think the answer is -3

?x+3=3(-x+7)

?x+3=-3x-21

?x = -3x-21-3

?x +3x = -24

(?+3) x = -24

the equation has no solutions if (?+3)=0
?+3=0
? = -3

Bryce has two small buckets each containing numbered tiles. The tiles in bucket A are the odd numbers from 1 to 31, one tile per number. The tiles in bucket B are the even numbers from 2 to 32, one tile per number. Bryce draws one tile from bucket A. On the number line below "Bucket A," select the point that represents the probability of drawing a tile that is a prime number from bucket A. He then draws one tile from bucket B. On the number line below "Bucket B," select the point that represents the probability of drawing a tile that is evenly divisible by 6 from bucket B.

Answers

A," select the point that represents the probability of drawing a tile that is a prime number from bucket A

total number of prime numbers in bucket A = 10( 3 5 7 11 13 17 19 23 29 31)

Probability = favorable outcomes/ total outcomes = 10/31

total number of numbers evenly divisible by 6 in bucket B = 5(6 12 18 24 30)

probability = 5/31

a 15-ft ladder is leaning against one wall of an alley 9 ft wide. the ladder slips, its top sliding down the wall, its foot sliding across the alley and striking the opposite wall at a speed of 4 ft/sec. How fast is the top of the ladder falling at that instance?

Answers

2x dx/dt +2y dy/dt = 0
x dx/dt + y dy/dt = 0
9*4 + 12 dy/dt = 0
dy/dt = - 3 ft/sec

The sum of three consecutive numbers is 57, what is the largest of these numbers

Answers

Answer:

Step-by-step explanation:

it is good

Jason ate one third of a pizza for dinner, and his brother ate one sixth of the same pizza.What portion of the pizza was left over?

Answers

One third = 2/6
2/6 + 1/6 = 3/6 = 1/2
They ate half a pizza.
That leaves the other half as the remainder

Jason and his brother ate a total of one half of the pizza when their portions, one third and one sixth respectively, are combined. Therefore, one half of the pizza was left over.

To calculate this, we add the fractions of the pizza that were consumed together:

Jason's portion: 1/3
Brother's portion: 1/6

We find a common denominator, which is 6 in this case, and sum the fractions:

(2/6) + (1/6) = 3/6

After simplifying 3/6, which is one half, we subtract this from the whole pizza to find the portion that is left:

1 - 1/2 = 1/2

Therefore, one half of the pizza was left over after Jason and his brother had their portions.

Someone plz help me with These questions :u have to solve for x and show work

4/9x+1/5x=87
-3.8x-5.9x=223.1
x+0.15x=3.45
-3/5x-7/10x+1/2x=-56

Answers

ok so the first one is
1.x=135
2.x=-23
3.x=3
4.x=70

If a quadrilateral has sides that measure 4 in. and angles that all measure 90°, we can consider the quadrilateral to be a/an

Answers

since all the sides are equal and the angles are 90 degrees
it would be a square

what value of x satisfies 3x + 2 = 14?

Answers

Hey!
Your answer would be 4!
3*4+2=14
Hope this helped! Make sure to check my calculations before submit!
Godspeed
-Song

x=4 3 times 4 equals 12 plus 2 is 14

What is 555.555 rounded to the nearest hundredth?

Answers

555.6 is the answer ahve a nice day

555.56 is the answer.

Player Points
Travis 6
Marcus 7
James 17
Taylor 2
Hector 1
Julio 22
Jonah 8
Chris 11
Scott 14

The chart shows the number of points different players scored during a game. What is the ratio of Julio's points to Jonah's points?
A) 1 : 2
B) 2 : 1
C) 4 : 11
D) 11 : 4

Answers

the answer is d 11:4

I believe the correct answer is D.

Which graph shows a proportional relationship?

Answers

Answer: The only graph that shows a proportional relationship is the line that crosses the origin point (0,0).

Explanation

The other graphs are linear functions but not not proportional relationships.

The general form of a proportional relationship is y = kx, where k is the proportionality constant. So, for x = 0 you will always obtain y = 0.

The general form of a linear relationshio is y = kx + b, being b the y-intercept, so if the y-intercept is not 0, it is not a proportional relationship. That is what happens with the other three graphs.

A graph that shows a proportional relationship include the following; A. graph A.

What is a proportional relationship?

In Mathematics and Geometry, a proportional relationship is a type of relationship that passes through the origin (0, 0) and produces equivalent ratios as represented by the following mathematical equation:

y = kx

Where:

y represents the y-variable.x represents the x-variable.k is the constant of proportionality.

In conclusion, the characteristics for a graph that shows a proportional relationship include the following:

A straight line can be drawn through its points.

The straight line connecting the points passes through the origin.

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what is the value of 4 in 546210

Answers

The value of 4 in 546210 is 40000.
To find the answer, you just need to understand one 'trick': replace al the following numbers with zeroes and delete the numbers which are in front of the number you are looking for, so: 546210 -> 540000 -> 40000
(In words, your answer is fourty thousand)

Hey! I am stuck on this, it's for class. I've been struggling with this for quite some time. So, if you have the chance. Click the picture and tell me if it's true or false using that table thingy. Now, you don't need do explain if you don't want to. But, I just need the answer, and yeah. Just tell me if it's true or false. Thanks!! :-)

Answers

true false false

your WELCOME;)

1. False
2. True
3. True

What is the area of a circle with a radius of 7?

Answers

A = pi r^2
A = 3.14 x 7^2
A = 3.14 x 49
A = 153.86

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