All categories

2 years ago

An object experiences two velocity vectors in its environment.

Mathematics

1 answer:

Andrej [43]2 years ago

5 0

Answer:

(a) 53.451∠163°

Step-by-step explanation:

The sum of the vectors is the sum of their components:

v1 +v2 = (-55i +3j) +(4i +13j) = (-55 +4)i +(3 +13)j = -51i +16j

<h3>conversion to polar form</h3>

This is converted to magnitude and direction by ...

|ai +bj| = √(a² +b²)

|-51i +16j| = √((-51)² +16²) = √(2601 +256) = √2857 ≈ 53.451

and

∠(ai +bj) = arctan(b/a) = arctan(16/-51) ≈ -17° +180° = 163°

note that 180° is added because the components indicate the angle is in the 2nd quadrant.

The object's speed and direction are ...

53.451 ∠163°

_____

<em>Additional comment</em>

If you're doing a lot of vector calculations, the process is simplified immensely by a suitable calculator. (See attached.) 2-dimensional vectors are handled nicely using the complex number functions of the calculator.

You might be interested in

You can pick a question to answer. You don't have to do all of them. Plz plz leave a explanation of how you did it. im strugglin

mariarad [96]

Answer:

-5

Step-by-step explanation:

do the exponets first. -6 squared is positive 36 because negative times a negative is a positive.

next you multiply 4 and 7 and get 28

you have 28-36+2 and that equals -5

6 0

3 years ago

Read 2 more answers

pavit has a clock with a minute hand that extends to the clock's edge. The minute hand is 5 inches long. What is the circumferen

Eddi Din [679]

Answer:

The circumference of the clock is $10\pi\ in$

Step-by-step explanation:

we know that

The circumference of a circle (clock) is equal to

$C=2\pi r$

In this problem

The long of the minute hand is the radius of the circle

$r=5\ in$

substitute

$C=2\pi (5)=10\pi\ in$ -----> exact value of the circumference

7 0

3 years ago

At the beginning of an environmental study, a forest covered an area of 1500 km2 . Since then, this area has decreased by 9.8% e

fredd [130]

Answer:

$A(t)=(0.902)^t \cdot 1500$ $[km^2]$

Step-by-step explanation:

In this problem, the initial area of the forest at time t = 0 is

$A_0 = 1500 km^2$

After every year, the area of the forest decreases by 9.8%: this means that the area of the forest every year is (100%-9.8%=90.2%) of the area of the previous year.

So for instance, after 1 year, the area is

$A_1 = A_0 \cdot \frac{90.2}{100}=0.902 A_0$