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4 years ago

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A person walks in the following pattern: 2.4 km north, then 1.9 km west, and finally 4.7 km south. (a) How far and (b) at what a

ngle (measured counterclockwise from east) would a bird fly in a straight line from the same starting point to the same final point?

1 answer:

enot [183]4 years ago

6 0

Answer:

a) Figure attached

b) For this case w have that A =(2.4 km)j, B= (-1.9 km) i , C= (-4.7 km)j

And the final position vector can be calculated adding the 3 vectors like this:

$s = A +B+C$

$s= (-1.9 km)i +(2.4 -4.7 km) j= (-1.9km)i + (-2.3 km)j$

We can find the magnitude of s like this:

$|s| = \sqrt{(-1.9)^2 +(-2.3)^2}=2.983$

And then we can find the angle with this formula:

$\theta = \tan^{-1} (\frac{-2.3 km}{-1.9 km})=50.44$

The other possibility is $\theta = 50.44+180 =230.44$

And since they want the angle measured from East the correct angle would be $\theta = 230.44$

Step-by-step explanation:

Part a

On the figure attached we have the vectors for the pattern described.

Part b

For this case w have that A =(2.4 km)j, B= (-1.9 km) i , C= (-4.7 km)j

And the final position vector can be calculated adding the 3 vectors like this:

$s = A +B+C$

$s= (-1.9 km)i +(2.4 -4.7 km) j= (-1.9km)i + (-2.3 km)j$

We can find the magnitude of s like this:

$|s| = \sqrt{(-1.9)^2 +(-2.3)^2}=2.983$

And then we can find the angle with this formula:

$\theta = \tan^{-1} (\frac{-2.3 km}{-1.9 km})=50.44$

The other possibility is $\theta = 50.44+180 =230.44$

And since they want the angle measured from East the correct angle would be $\theta = 230.44$

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$\dfrac{\mathrm dr}{\mathrm d\theta}=\dfrac{\mathrm d(\theta\sin\theta)}{\mathrm d\theta}+\dfrac{\mathrm d(\cos\theta)}{\mathrm d\theta}$

By the product rule,

$\dfrac{\mathrm d(\theta\sin\theta)}{\mathrm d\theta}=\dfrac{\mathrm d(\theta)}{\mathrm d\theta}\sin\theta+\theta\dfrac{\mathrm d(\sin\theta)}{\mathrm d\theta}=\sin\theta+\theta\cos\theta$

and

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So we have

$\dfrac{\mathrm dr}{\mathrm d\theta}=\sin\theta+\theta\cos\theta-\sin\theta$

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3 years ago

Henry bought an apple for $0.75, some apricots for $1.50, some cherries for $3.25, and three bananas for $1.50. Find the total c

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Answer:

$7.00

Step-by-step explanation:

cost of the apple: $0.75

cost of apricots: $1.50

cost of cherries: $3.25

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Add all the costs: $0.75 + $1.50 + $3.20 + $1.50 = $7.00

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4 years ago

A fish finder shows a large fish at 13 feet below the surface of the water and a smaller fish located 4 feet below the surface o

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Answer:

See Explanation

Step-by-step explanation:

The options are not given; However, the following explanation can guide you;

Represent the smaller fish with y and the bigger fish with x such that

$y = 13\ feet$

$x = 4\ feet$

The distance between them can be calculated using any of the following;

1.

$Distance = y - x$

This gives:

$Distance = 13 - 4$

$Distance = 9\ feet$

2.

$Distance = |y - x|$

$Distance = |13 - 4|$

$Distance = |9|$

$Distance = 9\ feet$

3.

$Distance = |x - y|$

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3 years ago

in 3 days Donald earned $42 running errands. he earned the same amount each day.how much did donald earn running errens each day

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4 years ago

Usha thinks that the area of the development will be greater than the total area of 50 football pitches.

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Answer:

Usha is correct

Step-by-step explanation:

See attachment

Given

Dimension of the development

$Height = \frac{1}{2}\ mile$

$Base = \frac{1}{2}\ mile$

Dimension of a football field

$Length = 100m$

$Width = 50m$

First, we calculate the area of the development.

Because it is triangular in shape, the area is:

$Area = \frac{1}{2} * Height * Base$

$Area = \frac{1}{2} * \frac{1}{2}mile * \frac{1}{2}mile$

Convert mile to meter

$Area = \frac{1}{2} * \frac{1}{2}* 1600m * \frac{1}{2} * 1600m$

$Area = \frac{1}{2} * 800m * 800m$

$Area = 400m * 800m$

$Area = 320000m^2$

The area of 50 football pitch is then calculated as:

$Area = 50 * Length * Width$

$Area = 50 * 100m * 50m$

$Area = 250000m^2$

By comparison:

$320000 > 250000$

<em>Hence, Usha's thought is correct</em>

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3 years ago