Use the definite integral and the Fundamental Theorem of Calculus to solve the following problem. A ball is thrown upward from a height of 1.2 m at an initial speed of 58 m/sec. Acceleration resulting from gravity is -9.8 m/sec^2. Find the following:

v(t)= _________
h(t)= ________

Answers

Answer 1

If v(t) and h(t) denote the ball's velocity and height at time t, respectively, then we have h(0) = 1.2 m and v(0) = 58 m/s.

The ball is in free fall after being tossed, so its acceleration is constant at any time t :

[tex]a(t) = -9.8 \dfrac{\rm m}{\mathrm s^2}[/tex]

By the fundamental theorem of calculus, the velocity function is given by

[tex]\displaystyle v(t) = v(0) + \int_0^t a(u) \, du[/tex]

Compute the integral:

[tex]\displaystyle v(t) = 58 \frac{\rm m}{\rm s} - \left(9.8 \frac{\rm m}{\mathrm s^2}\right) \int_0^t du[/tex]

[tex]\displaystyle v(t) = 58 \frac{\rm m}{\rm s} - \left(9.8 \frac{\rm m}{\mathrm s^2}\right) (t - 0)[/tex]

[tex]\displaystyle \boxed{v(t) = 58 \frac{\rm m}{\rm s} - \left(9.8 \frac{\rm m}{\mathrm s^2}\right) t}[/tex]

Similarly, the height function is given by

[tex]\displaystyle h(t) = h(0) + \int_0^t v(u) \, du[/tex]

[tex]\displaystyle h(t) = 1.2 \, \mathrm m + \int_0^t \left(58 \frac{\rm m}{\rm s} - \left(9.8 \frac{\rm m}{\mathrm s^2}\right) t\right) \, du[/tex]

[tex]\displaystyle h(t) = 1.2 \, \mathrm m + \left(58 \frac{\rm m}{\rm s}\right) (t - 0) - \frac12 \left(9.8 \frac{\rm m}{\mathrm s^2}\right) (t^2 - 0^2)[/tex]

[tex]\displaystyle \boxed{h(t) = 1.2 \, \mathrm m + \left(58 \frac{\rm m}{\rm s}\right) t - \frac12 \left(9.8 \frac{\rm m}{\mathrm s^2}\right) t^2}[/tex]

Answer 2

Answer:

V(t) = 58-9.8t

h(t)=1.2+58t-4.9[tex]t^{2}[/tex]

Step-by-step explanation:

Using the standard formula

a=V f-Vi/t --rearrange

at=V f-Vi

V f=V i + a t

therefore

V(t)=58-9.8t

same with height

H= Hi+Vit+1/2at^2

therefore

h(t)=1.2+58t-4.9t^2


Related Questions

Josh purchased a DVD for $10.80, before taxes. The price was after a 25% discount. What was the original price of the DVD?

Answers

Answer:

$

2.70

Step-by-step explanation:

A cell phone company charges a monthly fee plus $0.25 for each text message you send. The monthly fee is $30.00 . You owe $59.50. How many text messages did you send?

Answers

118 text messages.

59.50-30=29.5
29.5 divided by 0.25=118.

I hope this is right! :) Sorry if it isn’t!

Answer:

Excluding the monthly fee of $30 dollars.

Step-by-step explanation:

$30-$59.50 = $29.50

multiply $0.25 by 118 and you'll get exactly $29.50

the answer is " I sent 118 Text messages "

Define power of 10 rule

Answers

Answer:

A power of 10 is as many number 10s as indicated by the exponent multiplied together. ... Thus, shown in long form, a power of 10 is the number 1 followed by n zeros, where n is the exponent and is greater than 0; for example, 106 is written 1,000,000.

Step-by-step explanation:

Answer:

Power of 10, in mathematics, any of the whole-valued (integer) exponents of the number 10. A power of 10 is as many number 10s as indicated by the exponent multiplied together. ... When n is less than 0, the power of 10 is the number 1 n places after the decimal point; for example, 10−2 is written 0.01.

Step-by-step explanation:

Power of 10, in mathematics, any of the whole-valued (integer) exponents of the number 10. A power of 10 is as many number 10s as indicated by the exponent multiplied together. ... When n is less than 0, the power of 10 is the number 1 n places after the decimal point; for example, 10−2 is written 0.01.

Power of 10, in mathematics, any of the whole-valued (integer) exponents of the number 10. A power of 10 is as many number 10 sec as indicated by the exponent multiplied together. ... When n is less than 0, the power of 10 is the number 1 n places after the decimal point; for example, 10−2 is written 0.01.

1) Order the numbers from least to greatest.
=2
3
3.5
2.5
2
NI
PLEASE HELP

Answers

Answer:

2, 2, 2.5, 3, 3.5

Step-by-step explanation:

Answer:

2, 2.5, 3, 3.5

Even thought there are two "2's", you only list one making it 2,2.5,3,3.5 instead of 2,2,2.5,3,3.5

How many pounds is a pepper?
I really need to know.

Answers

Answer:

4-5 ounces or 113-142 grams

Step-by-step explanation:

Carl ordered $28 of pizza for dinner. About how much money
does he need, rounded to the nearest ten?

Answers

Answer:

30 dollars.

Step-by-step explanation:

What is 28 closer to? 20 or 30?

30.

He would have to pay 30$, and would get 2 dollars back in change.

I hope this helped at all.

2x-7=13
What is the answer for x ?

Answers

Answer:

The answer will be ( x = 10)

Please help I really need help if right you get Branly please help.

Answers

[1] 1/2

    - It will be 1/2 as large because of the scale factor

[2] 1/4

    - 1/2 * 1/2 = 1/4

[3] (1/2)n

    - For every scale factor (n), there will be a chance of 1/2

Have a nice day! - I know I answered this elsewhere, I saw it twice haha

  I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

PLZ ANSWER QUICK. WILL GIVE BRAINLY. NO EXPLANATION NEEDED.

Answers

Answer:

None of these are correct

Step-by-step explanation:

XZ = XY + YZ = 48 + 50 = 98

Write 27% as a fraction.​

Answers

Answer:

27/100

Step-by-step explanation:

27%= 0.27= 27/100 which cannot be reduced

Answer:

27/100

Step-by-step explanation:

27% = 27/100

I need help with this question

Answers

The answer is in the picture.

Brainliest would be appreciated.

the answer is 0 see the picture below to prove my answer thankyou :)


$1.800 is invested in account that earns 6% interest compounded quarterly, how much will this
investment be worth after 6 years Given : A =
P(1 + 3) "4
8
9
$2.573.11
$1,968.20
$7,288.08
$1,252.40
Question 5 (1 point)
Dan bou

Answers

Answer:

4 better inbox

Step-by-step explanation:

g(x)=(x-1)^3-1 find the inverse of this function

Answers

Answer:

G^−1(x)=3√x+1+1      

Step-by-step explanation:

Answer:

[tex]g^{-1}(x)[/tex]= [tex]\sqrt[3]{x+1}[/tex]+1

Step-by-step explanation:

To find the inverse, swap x and y.

g(x)=(x-1)^3-1

-> x=(y-1)^3-1

Solve the equation in terms of y.

x=(y-1)^3-1

x+1=(y-1)^3

[tex]\sqrt[3]{x+1}[/tex]=y-1

[tex]\sqrt[3]{x+1}[/tex]+1=y

can someone help me with these 3 pls?

Answers

The answer is definitely 21 cause yk 21

Write the correct order of the letters to the finish line

Answers

Answer:

Write the correct order of the letters to the finish line

Write the correct order of the letters to the finish line

2/3 of 40
3/5 of 45

Yeah so answer that

Answers

Hi,

[tex] \frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d} [/tex]

[tex] \frac{2}{3} \times \frac{40}{1} = \frac{80}{3} [/tex]

2/3 of 40:

80/3

[tex] \frac{3}{5} \times \frac{45}{1} = \frac{135}{5} = 27[/tex]

3/5 of 45:

27

✅(. ❛ ᴗ ❛.)

Answer:

A= 26.67

B= 27

Step-by-step explanation:

2/3 x 40 = 26.67

(2×40= 80÷3 = 26.67)

and...

3/5 x 45 = 27

(3×45= 135÷5=27)

Hope this helped you- have a good day bro cya)

Blue10
Brown15
Green5
Red10
Yellow12

The table shows how many of each color candy came out of a bag. What is the probability of choosing a brown candy?

Answers

15/52 is the probability

a dress which sosts $180 is being sold at a discoundof 10% the amount of the discount is

Answers

Answer:

The discount is $18.

5x-4=9x+6 please put explanation

Answers

1- first more the all the variables to the left side and change the sign.
So: 5x-9x=6+4
2- add/ subtract the terms. So: -4x=10
3- divide both sides by -4 to find x
So: -4x/-4 =10/-4
The answer will be: x= -2.5

19. There are 1,200 students at Thomas School, Each
day, students take 5 classes and teachers teach 4 classes. If each class
has 30 students and 1 teacher, how many teachers teach at the school?

Answers

Answer: 40 teachers

Step-by-step explanation:

Do 1,200 Divided by 30 because thats the amount of students

I thought of a number I called this number n I multiplied my number by the sum of 12 and 18 I added 43 to the result and I got 103 what is n equal to​

Answers

[tex](n \times (12 + 18)) + 43 = 103[/tex]

[tex]30n + 43 = 103[/tex]

Subtract both sides 43

[tex]30n + 43 - 43 = 103 - 43[/tex]

[tex]30n = 60[/tex]

Divide both sides by 30

[tex] \frac{30n}{30} = \frac{60}{30} \\ [/tex]

[tex]n = 2[/tex]

URGENT PLEASE DO!! will give brainliest to first person to answer

Answers

29293

Step-by-step explanation:

yes yes !!

Help me please
You need to find the measure of angle A
Most people don’t do this when I ask these questions

Answers

Answer:

Step-by-step explanation:

6x + 5 = 4x + 45

6x - 4x = 45 - 5

2x = 40

x = 20

6x + 5 = 6.20 + 5 = 125°

Amy drove to her mother's house, which is
204 miles away. If it took her 3 hours, what was
her average speed

Answers

Answer:  68 miles per hour 2

204 miles/3 hours = 68 miles per hour

i hope this helps you ok :)

Answer:

68 Miles Per Hour

Step-by-step explanation:

[tex]\frac{204}{3} =68[/tex]

Identify the slope and y-intercept of the
equation 2x + 5y = 20

Answers

Answer:

Slope = - ⅖

Y-intercept = (0, 4), where b = 4

Step-by-step explanation:

Given the linear equation in standard form, 2x + 5y = 20, where A = 2, B = 5, and C = 20:

Start by transforming the standard equation into its slope-intercept form, y = mx + b, where m = slope, and b = y-intercept.

Subtract 2x from both sides:

2x -2x + 5y = - 2x + 20

5y = -2x + 20

Divide both sides by 5 to isolate y:

[tex]\frac{5y}{5} = \frac{-2x + 20}{5}[/tex]

y = - ⅖x + 4 ⇒ This is the slope-intercept form where the slope, m = -⅖, and the y-intercept, b = 4.  The y-intercept is the point on the graph where it crosses the y-axis, and has coordinates of (0, b). The y-coordinate is the value of b in the slope-intercept form. Therefore, the y-intercept is (0, 4).

When a cold drink is taken from a refrigerator, its temperature is . After minutes in a room its temperature has increased to . What is the temperature of the drink after minutes

Answers

Answer:

Step-by-step explanation:

I NEED THE ANSWER ASAP. IM BEING TIMED

The following information is known about a savings account.
Time = 6 years
Interest rate = 1.9%
Principal = $850
What amount of total interest will be earned at the end of year 6?

Answers

Answer:

96.90

Step-by-step explanation:

I = PRT

T = 6

P = 850

I = 1.9% = 0.019

I = (850)(0.019)(6) = 96.90 <==

NEED ASAP PLSS


5+2x = 2x+6

Answers

You want to simplify ? or just find the value ?

This is a answer
For 5+2x=2x+6

-5(2x -3) + 4x = - 3x + 6

Answers

We have -5(2x-3) + 4x = -3x + 6
<=> -10x + 15 + 4x = -3x + 6
<=> -10x + 4x + 3x = 6 - 15
<=> -3x = -9
<=> x = 3

Ok done. Thank to me:>

5) Which table does NOT represent a function?

Answers

Answer: D does not represent a function.

Step-by-step explanation: I hope this helps you out.

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