Physics, 14.10.2019 13:30 rouseallie9428

Vector a⃗ points in the negative y direction and has a magnitude of 7 units. vector b⃗ has twice the magnitude and points in the positive x direction.

find the direction and magnitude of a⃗ +b⃗ .
express your answer as a whole number.

Answers: 2

Show answers

Answers

The magnitude of the vector $(\vec A+\vec B)$ is $\boxed{16 \text{ units}}$ and the direction of the vector $(\vec A+\vec B)$ is $\boxed{26.56^\circ\text{ anticlockwise}}$

Further Explanation:

$\Vec A$ points in the negative Y-direction and has a magnitude of $7\text{ units}$ , so we will show it as a line of length $7\text{ units}$ in negative Y-direction.

$\Vec B$ has twice the magnitude and points in the positive X-direction, so we will show it by a line of double the length as before in positive X-direction, as shown in the figure below.

According to Cartesian coordinate system, the resultant will start either from tail of $\vec A$ and ends at head of $\vec B$ and vice-versa.

Now, resultant will be given by

$\begin{aligned}\vec R&=\vec A+\vec B\\\vec R&=({-7\hat j+14\hat i})\\\end{aligned}$

Hence, the magnitude of resultant or of vector $\vec A + \vec B$ is given by:

$\begin{aligned}|{\vec R}|&=\sqrt{({7^2}+{14^2})}\\&=\sqrt{(49+196)}\\&=\sqrt{245}\\&=15.65{\text{ units}}\\\end{aligned}$

It can be expressed in whole number as:

$\boxed{|\vec R|=16\text{ units}}$

Now, the direction of the resultant vector $\vec R$ or of the vector $\vec A + \vec B$ is given by:

$\tan\theta=\dfrac{{|{\vec A}|}}{{|{\vec B}|}}$

Now, substituting the values of vector $\vec A$ and $\vec B$ :

$\begin{aligned}\tan\theta&=\dfrac{7}{{14}}\\\tan\theta&=0.5\\\theta&={\tan^{-1}}(0.5)\\&=\boxed{26.56^\circ}\\\end{aligned}$

Thus, the magnitude of the vector $(\vec A+\vec B)$ is $\boxed{16 \text{ units}}$ and the direction of the vector $(\vec A+\vec B)$ is $\boxed{26.56^\circ\text{ anticlockwise}}$

Learn More:

1. A vector A is added to B= 6i-8j

2. A head-on elastic collision between two particles

3. An astronaut takes her bathroom scale on moon where g=1.6 m/s2

Answer Details:

Grade: High School

Subject: Physics

Chapter: Vectors and Scalars

Keywords:

Vector, scalars, vector A, Vector B, addition, resultant, unit, magnitude, direction, positive, X-axis, Y- axis, negative, 7 units, 14 units, twice the magnitude.

Vector a⃗ points in the negative y direction and has a magnitude of 7 units. vector b⃗ has twice the

Answer from: Quest

graph slopes whilst gas cools, then it is flat whilst conensation to liquid happens, the coolong liquid then graphs as a slope when it solidifies graph is flat

latent heat

Answer from: Quest

Answer;

hot magma rises and pushes up toward the lithosphere, and as it cools it cycles back down toward the core to be heated again.

explanation; convection currents are the circular pathways taken by a fluid that enhances heat transfer by the process known as convection which occurs in fluids.convection currents transfer heat from one place to another by mass motion of a fluid. earth mantle is in a semi-liquid state and behaves like any other fluid, rising up from the bottom of the mantle after becoming hotter and less dense from heat of the earth's core, as the rock loses heat into the earth's crust it becomes cooler and more dense, then sinking back down to the core, then repeating the cycle.

Another question on Physics

Physics, 21.06.2019 19:00

1) sections 1, 2, and 10 are significant primarily because they suggest the likelihood that a) widow wycherly is actually the woman in the full-length portrait. b) dr. heidegger wants to include his guests in an experiment with the water. c) dr. heidegger plans to drink some of the water from the vase and needs witnesses. d) the guests will be asked to witness dr. heidegger's transformation when he drinks the water.

Answers: 1

Answer

Physics, 22.06.2019 05:30

Because light travels in a straight line and casts a shadow, isaac newton hypothesized that light is

Answers: 1

Answer

Physics, 22.06.2019 09:00

The material that keeps its new shape after it is stretched is called?

Answers: 1

Answer

Physics, 22.06.2019 09:20

Question 11 of 13 (1 point) jump to question: a stairway, ladder, or ramp must be present in excavations in which of the following situations? a. all trenches must have access/egress b. the trench is more than 15 feet wide but only 1 ½ feet deep c. the trench is more than 4 feet deep and the devices must be within 25 feet of all workers

Answers: 1

Answer

You know the right answer?

Vector a⃗ points in the negative y direction and has a magnitude of 7 units. vector b⃗ has twice the...

Questions