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


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Step-by-step explanation:

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Step-by-step explanation:

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Step-by-step explanation:

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Answers

We have -5(2x-3) + 4x = -3x + 6
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Ok done. Thank to me:>

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Answers

Answer:

The discount is $18.

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:

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[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)

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

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29293

Step-by-step explanation:

yes yes !!

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

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[1] 1/2

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[2] 1/4

    - 1/2 * 1/2 = 1/4

[3] (1/2)n

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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

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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.

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Answers

Answer:

2, 2, 2.5, 3, 3.5

Step-by-step explanation:

Answer:

2, 2.5, 3, 3.5

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Answers

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Answers

Answer:

27/100

Step-by-step explanation:

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

Answer:

27/100

Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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Answers

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Step-by-step explanation:

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Answers

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i hope this helps you ok :)

Answer:

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Step-by-step explanation:

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NEED ASAP PLSS


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You want to simplify ? or just find the value ?

This is a answer
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PLZ ANSWER QUICK. WILL GIVE BRAINLY. NO EXPLANATION NEEDED.

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Answers

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Step-by-step explanation:

Answer:

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Answers

Answer:

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Answers

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Excluding the monthly fee of $30 dollars.

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