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3 years ago

Describe a situation where an object has a changing velocity but constant speed.

1 answer:

8 0

To summarize, an object moving in uniform circular motion is moving around the perimeter of the circle with a constant speed. While the speed of the object isconstant, its velocity is changing. Velocity, being a vector, has a constantmagnitude but a changing direction.

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Given three vectors A = 24i + 33j, B = 55i - 12j and C = 2i + 43j (a) Find the magnitude of each vector. (b) Write an expression

slega [8]

Answer:

(a) , . and .

(b) $\vec A - \vec C=22 \hat i -10 \hat j$ .

Explanation:

Given that,

and

$\vec {C}=2 \hat i +43 \hat j$

(a) The magnitude of a vector is the square root of the sum of the square of all the components of the vector, i.e. for a ,.

So, the magnitude of the is

$|\vec A|=\sqrt {24^2+ 33^2}$

$\Rightarrow |\vec A|=\sqrt {1665}$

The magnitude of the is

$|\vec B|=\sqrt {55^2+ (-12)^2}$

$\Rightarrow |\vec B|=\sqrt {3169}$

And, the magnitude of the is

$|\vec C|=\sqrt {2^2+ 43^2}$

$\Rightarrow |\vec C|=\sqrt {1853}$

(b) The difference between the two vectors is the difference between the corresponding components of the vectors. So, the required expression of is

$\vec A - \vec C=(24 \hat i +33 \hat j) - (2 \hat i +43 \hat j)$

$\Rightarrow \vec A - \vec C=24 \hat i +33 \hat j - 2 \hat i -43 \hat j$

$\Rightarrow \vec A - \vec C=22 \hat i -10 \hat j$

$\vec A - \vec N=(24 \hat i +33 \hat j) - (55 \hat i -12 \hat j)$

$\Rightarrow \vec A - \vec B=24 \hat i +33 \hat j - 55\hat i +12 \hat j$

$\Rightarrow \vec A - \vec B=-31 \hat i +45 \hat j\;\cdots (i)$

The magnitude of is

$|\vec A - \vec B|=\sqrt {(-31)^2+55^2}$

$\Rightarrow |\vec A - \vec B|=\sqrt {3986}$

$\Rightarrow |\vec A - \vec B|=63.13$

Now, if a vector $\vec V= -\alpha \hat i +\beta \hat j$ in 3rd quadrant having direction $\theta$ with respect to $\hat i$ direction, than

in the anti-clockwise direction.

Here, from equation (i), for the vector $\vec A - \vec C$ , $\alpha=31$ and $\beta=45$ .

$\Rightarrow \theta = \pi-\tan ^{-1}\left(\frac {45}{31}\right)$

180°-55.44° [as \pi radian= 180°]

124.56° in the anti-clockwise direction.

(d) Vector diagrams for $\vec A +\vec B$ and $\vec A - \vec B$ has been shown

in the figure(b) and figure(c) recpectively.

Vector $\vec A - \vec B$ is in 3rd quadrant as calculated in part (c).

While Vector $\vec A +\vec B=(24 \hat i +33 \hat j)+(55 \hat i -12 \hat j)$

$\Rightarrow \vec A +\vec B=79 \hat i +21 \hat j$ , which is in 1st quadrant as both the components are position has been shown in figure(b).

6 0

3 years ago

600.0 mL of air is at 27.0 °C. What is the volume at 60.0 °C?

Temka [501]

The answer is 682 mL

3 0

3 years ago

When sugar is poured from the box into the sugar bowl, the rubbing of sugar grains creates a static electric charge that repels

WARRIOR [948]

Explanation:

In order to calculate the force, we will use the following formula.

F = $k \frac{q_{1}q_{2}}{r^{2}}$

where, $q_{1} = q_{2} = 3.0 \times 10^{-11} C$

r = $8.0 \times 10^{-5} m$

Therefore, we will put the given values into the above formula as follows.

F = $k \frac{q_{1}q_{2}}{r^{2}}$

= $9 \times 10^{9} \frac{3 \times 10^{-11} \times 3 \times 10^{-11}}{(8.0 \times 10^{-5})^{2}}$

= $1.265 \times 10^{-3}$ N

Thus, we can conclude that the given two grains will repel each other by a force of $1.265 \times 10^{-3}$ N.

6 0

3 years ago

What is the minimum allowed length for the runway?

vazorg [7]

v = u + a t => t = v/a = 65/3 sec

s = u t + 1/2 a t² = 1/2 * 3 * 65²/3² = 704.6 meters

hop it helps

3 0

3 years ago

Explain why the intensity of the light in a flashlight beam decreases as the flashlight moves farther away.

Karolina [17]

Ir=Initial Intensity/Area of spread=Io4πr2
Ir∝1r2

It is seen from this expression that intensity is inversely proportional to the square of the distance. As we move away from the light source the intensity decreases at the rate of square of the distance from the source.

Brightness being the perception of intensity. more the intensity more bright the object is perceived and vice versa.

7 0

3 years ago