A boat is traveling due North at 27mph. A current is flowing at a bearing of 60° west of south at 8mph. Find the actual speed and direction of the boat written in magnitude and direction form.
Answers
Answer: [tex]24.02\ mph[/tex]
Step-by-step explanation:
Given
Boat is traveling due to north at [tex]v_{bf}=27\ mph[/tex]
The current is flowing [tex]60^{\circ}[/tex] west of south at [tex]v_f=8\ mph[/tex]
Suppose the actual velocity of boat is [tex]\vec{v_b}[/tex]
In vector notation we can write
[tex]\Rightarrow \vec{v_{bf}}=\vec{v_b}-\vec{v_f}\\\\\Rightarrow \vec{v_b}=\vec{v_{bf}}+\vec{v_f}[/tex]
Flow of current can be written as
[tex]\Rightarrow \vec{v_f}=-8\sin 60^{\circ}\hat{i}-8\cos 60^{\circ}\hat{j}[/tex]
Insert the values of vectors
[tex]\Rightarrow \vec{v_b}=27\hat{j}-8\sin 60^{\circ}\hat{i}-8\cos 60^{\circ}\hat{j}\\\\\Rightarrow \vec{v_b}=-4\sqrt{3}\hat{i}+27\hat{j}-4\hat{j}\\\\\Rightarrow \vec{v_b}=-4\sqrt{3}\hat{i}+23\hat{j}[/tex]
Magnitude of the velocity is
[tex]=\sqrt{(4\sqrt{3})^2+(23)^2}\\=\sqrt{48+529}\\=24.02\ mph[/tex]
The actual direction and magnitude of the velocity of the boat is the sum of
the velocity of the boat and the velocity of the current both in vector form.
The actual velocity and direction of the boat are approximately 24.02 m/s at a bearing of 16.76° west of north.Reasons:
Direction of the boat = North
Speed of the both = 27 mph
Direction of the current = 60° west of south
Speed of the current = 8 mph
Required:
The actual speed and direction of the boat written in magnitude and
direction.
Solution:
The velocities given in vector form are;
Velocity of the boat, [tex]\vec {v}_{boat}[/tex] = 27·j
60° west of south = 30° south of west
Therefore;
Velocity of the current, [tex]\vec{v}_{current}[/tex] = -8 × cos(30°)·i - 8×sin(30°)·j
The actual velocity of the boat, [tex]\vec{v}_{actual}[/tex] = [tex]\mathbf{\vec {v}_{boat}}[/tex] + [tex]\mathbf{\vec{v}_{current}}[/tex]
Which gives;
[tex]\vec{v}_{actual}[/tex] = 27·j - 8 × cos(30°)·i - 8 × sin(30°)·j
[tex]\vec{v}_{actual}[/tex] = 23·j - (4·√3)·i
Therefore;
[tex]\vec{v} _{actual}[/tex] = -(4·√3)·i + 23·j
Which gives;
[tex]|v_{actual}|[/tex] = √((-4·√3)² + 23²) = √(577) ≈ 24.02
The magnitude of the velocity of the boat, [tex]\mathbf{|v_{actual}|}[/tex] ≈ 24.02 m/s
The actual direction of the boat, θ, is given by the arctangent of the ratio
of the vertical to the horizontal component of the velocity as follows;
[tex]\displaystyle \theta = arctan \left(\frac{23}{-4 \cdot \sqrt{3} } \right) \approx \mathbf{-73.24^{\circ}}[/tex]
Based on the horizontal and vertical component, the above angle θ is
approximately 73.24° relative to the negative x-axis, which is 90° - 73.24° =
16.76° west of north.
Therefore;
The actual direction of the both is on a bearing of approximately 16.76° west of north.Learn more about vector quantities here:
https://brainly.com/question/1614684
Related Questions
What is the equation of the line that passes through (3.-1) and is parallel to the line y = 3x + 2?
Answers
Answer:
[tex]y=3x-10[/tex]
Step-by-step explanation:
Hi there!
What we need to know:
Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)Parallel lines always have the same slope and different y-intercepts1) Determine the slope (m)
[tex]y = 3x + 2[/tex]
From the given line, we can identify clearly that 3 is in the place of m, making it the slope. Because parallel lines have the same slope, the line we're solving for will also have a slope of 3. Plug this into [tex]y=mx+b[/tex]:
[tex]y=3x+b[/tex]
2) Determine the y-intercept (b)
[tex]y=3x+b[/tex]
Plug in the given point (3,-1)
[tex]-1=3(3)+b\\-1=9+b[/tex]
Subtract 9 from both sides
[tex]-1-9=9+b-9\\-10=b[/tex]
Therefore, the y-intercept of the line is -10. Plug this back into [tex]y=3x+b[/tex]:
[tex]y=3x-10[/tex]
I hope this helps!
In a school of 3200 total students 3/8
are boys &
rest girls, then,
i) Find the number of boys and girls.
ii) Find the percentages of boys and girls
Answers
Answer:
ii) Find the percentage of boys/girls
Step-by-step explanation:
If im incorrect please comment here ------------》
Does anyone understand? Need help asap
Answers
Answer:
it's 149.(54)=7
Step-by-step explanation:
that's the answer
Which of the following is equivalent to the expression below?
(– 3m + 5) + (m – 11)
A: – 2m – 6
B: 2m – 16
C: 4m – 16
D: – 4m – 6
Answers
Answer:
B
Step-by-step explanation:
Please help me on this problem
Answers
Answer:
The answer would be 20 mi
Step-by-step explanation:
a^2+b^2=c^2
a^2=144
b^2=256
C^2=400
Then you find the square root of ABC to find that C is 20
Hari's weekly allowance varies depending on the number of chores he does. He received $24 in allowance the week he did 16 chores, and $18 in allowance the week he did 4 chores. Write an equation for his allowance in slope-intercept form.
i need help!
Answers
Answer:
y = (1/2)x + 16
Step-by-step explanation:
General point/slope form is
y = mx +b (the two points given are (4,18) and (16,24))
slope = rise/run = (24-18)/(16-4) = 6/12 = 1/2
y = (1/2)x + b
pick one point (4,18) and plug in
18 = (1/2)4 + b
18 = 2 + b
b = 16 (he still gets $16 for zero chores)
So
y = (1/2)x + 16
4) What is the domain of the function?
Please help
Answers
Answer:
-4 <= x <= 5.
Step-by-step explanation:
For the end points, we usually colour it same as the ink, in blue, to mean inclusion. Here it is red, but we will assume inclusion as well, since exclusion will not have any correct answer.
Domain consists of all the valid values of x that apply to the function, which is from -4 to 5 inclusively. We will not exclude non-integer values because this is what the graph indicates.
The only valid answer is therefore the first one, -4 <= x <= 5.
Arthur competed in three different races. His time in the first race was 14.48 seconds, his time in the
second race was 26.35 seconds, and his time in the third race was 53.89 seconds. What was Arthur's
total time, in seconds, for all three races?
A: 83.52
B: 84.72
C: 93.52
D: 94.72
Answers
83.52
A
Step-by-step explanation:
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What is the value of angle vux
Answers
==============================================
There are two ways to do this.
The quicker way is to use the remote interior angle theorem. We have the interior angles 53 and 103 which add to 53+103 = 156 which is exactly the exterior angle VUX.
---------------
The slightly longer way involves finding angle TUV first. Let's say this is equal to the variable y
Adding any three interior angles of a triangle always gets us 180
53+103+y = 180
y+156 = 180
y = 180-156
y = 24
Angle TUV is 24 degrees
The angle supplementary and adjacent to this is angle VUX, which I'll call z
z+y = 180
z = 180-y
z = 180-24
z = 156
So this is another way to get to the answer 156 degrees.
what is the soultion 3-6x = 9-6x
Answers
Answer:
x=-6
Step-by-step explanation:
3-9= -6x+6x
x=-6
ans=-6
Find the value of x
I give you 10 points if you help
Answers
Step-by-step explanation:
x = 55
I hope this is helpful
What is the product of 3.8\times 10^23.8×10
2
and 6.4 \times 10^66.4×10
6
expressed in scientific notation?
Answers
Answer:
2.432 * 10⁹
Step-by-step explanation:
Given the expression;
3.8*10² × 6.4*10⁶
= (3.8*6.4)× (10²*10⁶)
= 24.32*10⁸
= 2.432* 10¹ * 10⁸
= 2.432 * 10⁹
Hence the product expressed as a scientific notation is 2.432 * 10⁹
the cost to go bowling is a function in terms of the number of games bowled. the cost to bowl 2 games with a shoe rental is $16.50. the cost to bowl 4 games with a shoe rental is $28.50. what is the cost of renting shoes?
Answers
Answer:
x = cost of games bowled = $6
y = cost of shoe rental = $4.50
Step-by-step explanation:
Let
x = cost of games bowled
y = cost of shoe rental
2x + y = 16.50 (1)
4x + y = 28.50 (2)
Subtract (1) from (2) to eliminate y
4x - 2x = 28.50 - 16.50
2x = 12
x = 12/2
x = 6
Substitute x = 6 into (1)
2x + y = 16.50 (1)
2(6) + y = 16.50
12 + y = 16.50
y = 16.50 - 12
y = 4.50
x = cost of games bowled = $6
y = cost of shoe rental = $4.50
Find the value of x, when log 10x + log 2 = log 60
Answers
Answer:
x = 3
Step-by-step explanation:
log 10x + log 2 = log 60
Subtract log 2 from each side
log 10x + log 2 -log 2 = log 60 - log 2
log 10x = log 60 - log 2
We know that log a - log b = log (a/b)
log 10 x = log (60/2)
log 10x = log 30
We know log a = log b that a = b
10x = 30
Divide by 10
10x/10 = 30/10
x =3
HELP PLS MATH !!!!!!!!!!!!!!
Answers
fraction form : 8/25
decimal form : 0.32
Answer:
8/25 or if you have to do decimal form it's 0.32
Step-by-step explanation:
If there were 199 million American adults in 1996, how many of them were obese? Round to the nearest million adults.
Answers
Write an equation of the line with slope -1 passing through (8,5).
Answers
Answer:
y = -1x + 13
Step-by-step explanation:
y = -1x + b
5 = -1(8) + b
5 = -8 + b
13 = b
Which type of line of symmetry does the figure have?
Answers
In order to solve by completing the square, what value needs to be added to both sides of the equation:
Answers
Answer:
The answer is "[tex](x + 8)^2 = 58[/tex]"
Step-by-step explanation:
Let the equation is:[tex]x^2+16x=-6[/tex]
by adding and subtracting 64 then:
[tex]x^2 + 16x + 64 = -6 + 64\\\\x^2 + 2\times x\times 8 + 64 = -6 + 64\\\\ (x + 8)(x + 8) = 58\\\\ (x + 8)2 = 58[/tex]
Simplify 2/3(9x−15)−(−6x+2) . Write your answer in factored form.
Answers
The value of the expression 2/3(9x−15)−(−6x+2) is 12(x - 1).
How to calculate the expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.
H we, we want to simplify 2/3(9x−15)−(−6x+2). This will be illustrated thus:
2/3(9x−15)−(−6x+2) .
= (6x - 10) + 6x - 2
= 6x - 10 + 6x - 2
= 12x - 12
= 12(x - 1)
Learn more about expressions on:
brainly.com/question/723406
#SPJ1
Line t intersects line u, as shown below.
11
(2x +17)
125°
What is the value of x?
A 54
B
71
С
108
125
Answers
9514 1404 393
Answer:
A. 54
Step-by-step explanation:
The two marked angles are "vertical angles," so are congruent.
125° = (2x +17)°
108 = 2x . . . . . . . . divide by °, subtract 17
54 = x . . . . . . . . . . divide by 2
Answer:
x=54
Step-by-step explanation:
2x+17 will be kept equal to 125
so 2x+17=125
2x=125-17
2x=108
x=[tex]\frac{108}{2}[/tex]
x=54 ans
hi pls help i’ll give brainliest
Answers
Answer:
B if I remember correctly.
The school cafeteria sells two kinds of wraps: vegetarian and chicken. The vegetarian wrap costs $1.00 and the chicken wrap costs $2.70. Today they made $244.60 from the 146 wraps sold. How many of the wraps sold were vegetarian?
Answers
Answer:
88 Vegetarian Wraps Sold.
Step-by-step explanation:
This is a System of Equations Problem.
Your Two Systems Are:
v(1)+c(2.7)=244.6 and c+v=146
c = chicken wraps and v = vegetarian wraps
Each chicken wrap costs $2.70 (2.7). Put the variable of c next to (2.7) meaning to multiply.
Each vegetarian wrap costs $1 (1). Put the variable of v next to (1)
244.60 (244.6) is the total amount of money made from selling the wraps. This will be the total of the equation.
v(1)+c(2.7)=244.6
Solve 2.7c+v=244.6 for v.
Add -2.7c to both sides.
2.7c+v+−2.7c=244.6+−2.7c
v=−2.7c+244.6
Substitute −2.7c+244.6 for v in c+v=146.
c+v=146
c+−2.7c+244.6=146
Simplify both sides of the equation.
−1.7c+244.6=146
Add -244.6 to both sides.
−1.7c+244.6+−244.6=146+−244.6
−1.7c=−98.6
Divide both sides by -1.7.
[tex]\frac{-1.7c}{-1.7} =\frac{-98.6}{-1.7}[/tex]
c=58
Substitute 58 for c in v=−2.7c+244.6.
v=−2.7c+244.6
v=(−2.7)(58)+244.6
Simplify both sides of the equation.
v=88
Answer:
c=58 and v=88
88 vegetarian wraps were sold.
I NEED HELP WITH THIS ONE TOO!
Answers
4 × ( 4 + 9 ) = 2 × ( 2 + x )
4 × 13 = 2 × ( 2 + x )
2 × 2 × 13 = 2 × ( 2 + x )
2 × 26 = 2 × ( 2 + x )
Divide both sides by 2
2 × 26 ÷ 2 = 2 × ( 2 + x ) ÷ 2
26 = 2 + x
Subtract both sides 2
26 - 2 = 2 - 2 + x
x = 24
Solve for x Show your work
Answers
Answer:
x = 12
Step-by-step explanation:
To solve this and show your work, you have to start of with the equation (3x - 6) = 30.
You then have to add 6 to both sides like this:
[tex](3x - 6) = 30 \\ \: \: \: \: \: \: \: \: \: \: + 6 \: \: \: \: \: + 6 [/tex]
So then the 6 is cancelled out, and you are left with
3x = 36.
Now you just have to divide both sides by 3 like this:
[tex] \frac{3x}{3} = \frac{36}{3} [/tex]
Which cancels 3 out, and you are left with
x = 12.
You want to buy a new HD TV for $454.95. The salesperson says if you buy the weekend of Father's day you can get a 15% discount. Find the following.
The Discount = enter how much you will save, not the percentage.
Price after Discount =
Sales Tax = (Use a sales tax of 8.25%)
Total Cost =
Answers
Answer:
See below.
Step-by-step explanation:
454.95x.15=68.24 DISCOUNT
454.95-68.24=386.71 Price After Discount
386.71x.0825=31.91 Sales Tax
386.71+31.91=418.62 Total Cost
Find the equation of the line passing through the point (-2,5)
that is perpendicular to the line 6x + 2y = 8.
Answers
Answer:
y = 1/3x + 17/3
Step-by-step explanation:
6x + 2y = 8
2y = -6x + 8
y = -3x + 4
y = 1/3x + b
5 = 1/3(-2) + b
5 = -2/3 + b
17/3
I rly need yalls help on #1-3, and 5 pleasee!
Answers
GEOMETRY/WILL MARK BRAINLIST
GOD BLESS WHAT IS THE ANSWER TO THIS?
Answers
Answer:
Option 1
Step-by-step explanation:
It's asking me to write 20 words so blah blah blah.
Is 2.99 irrational or rational?
Answers
Answer:
rational
Step-by-step explanation:
its decimal expansion terminates after 9 and it can also be represented as fraction.
Answer:
Rational
Step-by-step explanation:
Irrational numbers are numbers that cannot be written as a fraction (denominator of 1 does not count). 2.99 can easily be written as a fraction (e.g. [tex]\frac{299}{100}[/tex]) and therefore is rational.