The velocity-time table represents the motion of a rightward-

A cyclist makes the following trip along two vectors; he travels 9km to the north and then travels 6km to the east

Answer:

Final distance from the origin: 10.82 km. the vector points as shown in the attached image.

Angle with respect to the east: $56.31^o$

Explanation:

Please refer to the attached image. The cyclist's trip is indicated with the green arrows (9 km to the north followed by 6 km to the east.

So his final position is at the tip of this last vector, and indicated by the orange vector drawn form the point where the trip starts to the cyclist's final location.

We observe that this orange vector is in fact the hypotenuse of a right angle triangle, and we can estimate the distance from the origin by the Pythagorean theorem:

$d=\sqrt{9^2+6^2} \\d=\sqrt{81+36} \\d=\sqrt{117} \\d=10.82 \,\,km$

Notice that this is NOT the actual number of km that the cyclist pedaled to reach the final point.

Now, to find the value of the angle $\theta$ , we need to use trigonometry, and in particular the tangent function gives us the ratio between the side of the triangle "opposite" to the angle, divided the side "adjacent" to the angle:

$tan(\theta)=\frac{opp}{adj} \\tan(\theta)=\frac{9}{6}\\tan(\theta)=\frac{3}{2}\\$

Now we can find the value of the angle by using the arctan function:

$tan(\theta)=\frac{3}{2} \\\theta=arctan(\frac{3}{2} )\\\theta= 56.31^o$

6 0

3 years ago

What is science and why do we study science and what are the benefits we are going to get from it ?

Nina [5.8K]

Answer:

science is define as the study of physics, chemistry, biology, geology and astronomy. science is very important in our daily life.we study science for knowing the knowledge about biological and chemical and many other aspects.without science it is impossible to live our daily life.science is used in each and every steps.

Explanation:

There are many more benefits that we are getting and going to get . Science has already discovered many things ,that we didn't expect efore.And also in progress to discover new things.Science has developed a new type of antivirus that protect us from different virus.Has made different medicine that recover a people. So it is very useful in our life.

4 0

2 years ago

Given two vectors A--> = 4.20 i^+ 7.20 j^ and B--> = 5.70 i^− 2.40 j^ , find the scalar product of the two vectors A-->

Arisa [49]

Answer:

$\vec{A}\times \vec{B}=-51.12\hat{k}$

$\theta=83.2^{\circ}$

Explanation:

We are given that

$\vec{A}=4.2\hat{i}+7.2\hat{j}$

$\vec{B}=5.70\hat{i}-2.40\hat{j}$

We have to find the scalar product and the angle between these two vectors

$\vec{A}\times \vec{B}=\begin{vmatrix}i&j&k\\4.2&7.2&0\\5.7&-2.4&0\end{vmatrix}$

$\vec{A}\times \vec{B}=\hat{k}(-10.08-41.04)=-51.12\hatk}$ $\hat{k}$

Angle between two vectors is given by

$sin\theta=\frac{\mid a\times b\mid}{\mid a\mid \mi b\mid}$

Where $\theta$ in degrees

$\mid{\vec{A}}\mid=\sqrt{(4.2)^2+(7.2)^2}=8.3$

Using formula $\mid a\mid=\sqrt{x^2+y^2}$

Where x= Coefficient of unit vector i

y=Coefficient of unit vector j

$\mid{\vec{B}}\mid=\sqrt{5.7)^2+(-2.4)^2}=6.2$

$\mid{\vec{A}\times \vec{B}}\mid=\sqrt{(-51.12)^2}=51.12$

Using the formula

$sin\theta=\frac{51.12}{8.3\times 6.2}=0.993$

$\theta=sin^{-1}(0.993)=83.2$ degrees

Hence, the angle between given two vectors= $83.2^{\circ}$

7 0

4 years ago

A bus is designed to draw its power from a rotating flywheel that is brought up to 3000 rpm by an electric motor. The flywheel i

Arada [10]

To solve this problem we will apply the concept of rotational kinetic energy. Once this energy is found we will proceed to find the time from the definition of the power, which indicates the change of energy over time. Let's start with the kinetic energy of the rotating flywheel is

$E_r = \frac{1}{2} I\omega^2$

Here

I = moment of inertia

$\omega =$ Angular velocity

Here we have that,

$\omega = 3000\frac{rev}{min}(\frac{2\pi rad}{1rev})(\frac{1min}{60s})$

$\omega = 314.159rad/s$

Replacing the value of the moment of inertia for this object we have,

$E_r = \frac{1}{2} (\frac{MR^2}{2})\omega^2$

$E_r = \frac{1}{2} (\frac{2000(0.5)^2}{2})(314.159)^2$

$E_r = 1.233698*10^7J$

The expression for average power is

$P = \frac{E_r}{\Delta t}$

$\Delta t = \frac{E_r}{P}$

$\Delta t = \frac{1.233698*10^7}{20*10^3}$

$\Delta t = 616.8s \approx 620s$

Therefore the correct answer is 620s.

3 0

4 years ago

Is the study of muscle movement in the human body and example of biology and physics

Thepotemich [5.8K]

Yes, in broader terms for people who actually study this, this is called biomechanics. Bio refers to the human body and it moving, while the physics part comes in when a ball is thrown for example and you want to know how far it is thrown.

3 0

4 years ago