Mathematics, 04.06.2020 13:09 alinegonzalez0027

A car travels 10km southeast and then 15 km in a direction 60 degrees north of east. What is the magnitude of the car's resultant vector?

Answers: 2

Show answers

Answers

Answer from: saren47

The magnitude of the car's resultant vector is 15.72.

Given that,

A car travels 10km southeast,

And then 15 km in a direction 60 degrees north of east.

We have to find,

The magnitude of the car's resultant vector.

According to the question,

To resultant direction calculate by using the sum of vectors following all the steps given below.

A car travels 10 km southeast,

And then 15 km in a direction 60 degrees north of east.

The first vector has module is 10 and angle is 315°,

In the south direction, the angle is 270° and east is 360°,

So the angle in southeast,

$\rm = \dfrac{270+360}{2}\\\\= \dfrac{630}{2}\\\\= 315 \ degree$

The second vector has module 15 and angle = 40°

Decompose both vectors in their horizontal and vertical component:

The horizontal component of the first vector is,

$\rm = 10 \times cos(315) = 10 \times 0.70= 7.07$

The vertical component of the first vector is,

$= \rm 10 \times sin(315) = -7.07$

The horizontal component of the second vector is,

$\rm = 15 \times cos(60) = 15 \times 0.5= 7.5$

The vertical component of the second vector is,

$\rm = 15 \times sin(40) = 15 \times 0.86= 12.99$

The sum of the horizontal component of the resultant vector is,

= 7.07+7.5=14.57

And the sum of the vertical component of the resultant vector is,

= -7.07+12.99=5.91

The magnitude of the vector (14.57km, 5.91km) is:

Therefore,

The magnitude of the car's resultant vector is,

$\rm Resulatant = \sqrt{(14.57)^2+ (5.91)^2}\\\\ Resulatant = \sqrt{212.28+ 34.92} \\\ \\ Resulatant = \sqrt{247.20}\\\\ Resulatant = 15.72$

Hence, The required magnitude of the car's resultant vector is 15.72.

For more details refer to the link given below.

link

Answer from: DESIRE44030

15.85km

Step-by-step explanation:

The car starts at the point (0,0)

Let's define east as the positive x-axis and north as the positive y-axis.

first, the car travels 10km southeast, so the angle is -45° from the east.

Then the new position of the car is:

(10km*cos(-45°), 10km*sin(-45°)) = (7.07km, -7.07km)

Now, from this point the car travels 15km with an angle of 60° (counting from the east)

So the new position is:

(7.07km + 15km*cos(60°), -7.07km + 15km*sin(60°)) = (14.57km , 5.91km)

The magnitude of a vector (x, y) is √(x^2 + y^2)

So the magnitude of the vector (14.57km , 5.91km) is:

√((14.57km)^2 + (5.91km)^2) = 15.85km

Answer from: Quest

29. because you will divide each number of months by 12 to find the number of years. which would mean, 5, 12.5, 16, 45, 50, 72.5. which is crazy. anyhow, i think you find the median in the middle. and yea hope your test goes good

Answer from: Quest

step-by-step explanation:

bob the banana

Another question on Mathematics

Mathematics, 21.06.2019 15:30

Will mark brainliest if you answer ! the taco shop sold 198 lunches friday. this number is 3 more than 3 times the number they sold monday. let n represent the number of lunches sold monday. which equation shows an equality between two different ways of expressing the number of lunches sold on friday? a. n – 3 = 198 b. 3n – 3 = 198 c. 3n + 3 = 198 d. n + 3 = 198

Answers: 1

Answer

Mathematics, 21.06.2019 16:30

Translate this phrase into an algebraic expression. 21 more than twice goran's savings use the variable g to represent goran's savings. need to know fast.

Answers: 1

Answer

Mathematics, 21.06.2019 19:30

You have 17 cats that live in houses on your street, 24 dogs, 3 fish, and 4 hamsters. what percent of animals on your block are dogs?

Answers: 2

Answer

Mathematics, 21.06.2019 21:30

Can someone explain to me how to do

Answers: 1

Answer

You know the right answer?

A car travels 10km southeast and then 15 km in a direction 60 degrees north of east. What is the mag...