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uppose a small cannonball weighing 16 pounds is shot vertically upward, with an initial velocity v0 = 290 ft/s. The answer to the question "How high does the cannonball go?" depends on whether we take air resistance into account. If air resistance is ignored and the positive direction is upward, then a model for the state of the cannonball is given by d2s/dt2 = −g (equation (12) of Section 1.3). Since ds/dt = v(t) the last differential equation is the same as dv/dt = −g, where we take g = 32 ft/s2. If air resistance is incorporated into the model, it stands to reason that the maximum height attained by the cannonball must be less than if air resistance is ignored. (a) Assume air resistance is proportional to instantaneous velocity. If the positive direction is upward, a model for the state of the cannonball is given by m dv dt = −mg − kv, where m is the mass of the cannonball and k > 0 is a constant of proportionality. Suppose k = 0.0025 and find the velocity v(t) of the cannonball at time t.

Answers

Answer 1

Answer:

Answer:

Given in the explanation

Step-by-step explanation:

Given

w = 16 pounds

v₀ = 290 ft/s

g = 32 ft/s²

k = 0.0025 (Kg/s)

$m(dv)/(dt)= -mg - kv^(2)$

Solving the differential equation we obtain

$v(t)=((1)/(0.0125))*tan((-2*(t+C_(1) )/(5) )$

If v(0) = 290 ft/s, we have

$290=((1)/(0.0125))*tan((-2*(0+C_(1) )/(5) )$

⇒ C₁ = -3.254

Finally, we have

$v(t)=((1)/(0.0125))*tan((-2*(t-3.254 )/(5) )$

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Which is an example of an incremental approach to solving a problem? writing the program code of the solution informally representing the steps of a solution in a flowchart representing the code of the solution in different programming languages writing the steps of a solution in small pieces of code

Answers

Answer:

writing the steps of a solution in small pieces of code

Step-by-step explanation:

edg 2020

Answer:

D on edge :)

Step-by-step explanation:

SIMPLE GRAPHING EQUATION (CORRECT ANSWER = BRAINLIEST, THANKS, 5 STAR, AND A COMMENT + THE POINTSFind the value of “b” so that the slope of the line passing through the points A(5, –8) and B(–1, b) is –2.

Answers

Answer:

b=4

Step-by-step explanation:

For this question we need to know the formula of slope that is m which is

$m=(y_2-y_1)/(x_2-x_1)$

where $(x_1,y_1) , (x_2,y_2)$ are the points $(5,-8),(-1,b)$ respectively

and hence we have the value of m= -2 which is the slope we simply plug in all the values.

$m=(y_2-y_1)/(x_2-x_1)\n\n-2=(b-(-8))/(-1-5) \n\n-2=(b+8)/(-6) \n\n12=b+8\n12-8=b\n4=b$

So the value of b=4

Answer:

b is 4

Step-by-step explanation:

Several steps are required to find this answer. You need to use the information you are given as well as the formula y=mx+b. You are given the slope and one of the coordinates. Plug the information into the formula to find b, which is the constant.

The point given is (5,-8)

The slope given is -2

Plug the x and y into y=mx+b

-8=-2(5)+b

-8=-10+b

-8+10=b

b=2

Now that you have the full equation, y=-2x+2 , you can plug in the x-coordinate of the other coordinate to find the missing y-value.

y=-2(-1)+2

y=2+2

y=4

Therefore, the b you are solving for is 4.

Help me please need help

Answers

The slow is equal to 4

-1 7/9 is the same as them sum of -2 5/6 and 1/3 times a number. what is the number?

Answers

-1 7/9= -2 5/6 + 1/3x
+2 5/6 to each side
-1 7/9 + 2 5/6 = 1 1/18

1 1/18 = 1/3x
Divide each side by 1/3

Answer is 3 1/6

Help please!!!!! asap

Answers

Answer:

$w \leq \: 26$

Step-by-step explanation:

$(9w - 4)/(5) \leq (7w + 2)/(4)$

First of all cross multiply

That's

$4(9w - 4) \leq5(7w + 2)$

Expand the terms

$36w - 16 \leq \: 35w + 10$

Add 16 to both sides

That's

$36w + 16 - 16 \leq \: 35w + 10 + 16 \n 36w \leq35w + 26$

Subtract 35w from both sides

We have

$36w - 35w \leq35w - 35w + 26 \n$

We have the final answer as

$w \leq \: 26$

Hope this helps you

Karen earns $54.60 for working 6 hours. If the amount she earns varies directly with thenumber of hours she works, how many hours would she need to work to earn an
additional $260?

Answers

Given:

Karen earns $54.60 for working 6 hours.

Amount she earns varies directly with the number of hours she works.

She need to work to earn an additional $260.

To find:

Number of hours she need to work to earn an additional $260.

Solution:

Let the amount of earnings be A and number of hours be t.

According to question,

$A\propto t$

$A=kt$ ...(i)

where, k is constant of proportionality.

Karen earns $54.60 for working 6 hours.

$54.60=k(6)$

Divide both sides by 6.

$(54.60)/(6)=k$

$9.1=k$

Put k=9.1 in (i).

$A=9.1t$

Substitute A=260 in the above equation.

$260=9.1t$

Divide both sides by 9.1.

$(260)/(9.1)=t$

$28.5714=t$

$t\approx 29$

Therefore, she need to work extra about 29 hours to earn an additional $260.

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