We now have the tools to solve the problem we introduced in the opening of the section.
An airplane is flying at an airspeed of 200 miles per hour headed on a SE bearing of 140°. A north wind (from north to south) is blowing at 16.2 miles per hour. What are the ground speed and actual bearing of the plane? See
[link] .
The ground speed is represented by
in the diagram, and we need to find the angle
in order to calculate the adjusted bearing, which will be
Notice in
[link] , that angle
must be equal to angle
by the rule of alternating interior angles, so angle
is 140°. We can find
by the Law of Cosines:
The ground speed is approximately 213 miles per hour. Now we can calculate the bearing using the Law of Sines.
Therefore, the plane has a SE bearing of 140°+2.8°=142.8°. The ground speed is 212.7 miles per hour.
The position vector has its initial point at the origin. See
[link] .
If the position vector is the same for two vectors, they are equal. See
[link] .
Vectors are defined by their magnitude and direction. See
[link] .
If two vectors have the same magnitude and direction, they are equal. See
[link] .
Vector addition and subtraction result in a new vector found by adding or subtracting corresponding elements. See
[link] .
Scalar multiplication is multiplying a vector by a constant. Only the magnitude changes; the direction stays the same. See
[link] and
[link] .
Vectors are comprised of two components: the horizontal component along the positive
x -axis, and the vertical component along the positive
y -axis. See
[link] .
The unit vector in the same direction of any nonzero vector is found by dividing the vector by its magnitude.
The magnitude of a vector in the rectangular coordinate system is
See
[link].
In the rectangular coordinate system, unit vectors may be represented in terms of
and
where
represents the horizontal component and
represents the vertical component. Then,
v = a
i + b
j is a scalar multiple of
by real numbers
See
[link] and
[link] .
Adding and subtracting vectors in terms of
i and
j consists of adding or subtracting corresponding coefficients of
i and corresponding coefficients of
j . See
[link] .
A vector
v =
a
i +
b
j is written in terms of magnitude and direction as
See
[link] .
The dot product of two vectors is the product of the
terms plus the product of the
terms. See
[link] .
We can use the dot product to find the angle between two vectors.
[link] and
[link] .
Dot products are useful for many types of physics applications. See
[link] .
Questions & Answers
Three charges q_{1}=+3\mu C, q_{2}=+6\mu C and q_{3}=+8\mu C are located at (2,0)m (0,0)m and (0,3) coordinates respectively. Find the magnitude and direction acted upon q_{2} by the two other charges.Draw the correct graphical illustration of the problem above showing the direction of all forces.
To solve this problem, we need to first find the net force acting on charge q_{2}. The magnitude of the force exerted by q_{1} on q_{2} is given by F=\frac{kq_{1}q_{2}}{r^{2}} where k is the Coulomb constant, q_{1} and q_{2} are the charges of the particles, and r is the distance between them.
Muhammed
What is the direction and net electric force on q_{1}= 5µC located at (0,4)r due to charges q_{2}=7mu located at (0,0)m and q_{3}=3\mu C located at (4,0)m?
Capacitor is a separation of opposite charges using an insulator of very small dimension between them. Capacitor is used for allowing an AC (alternating current) to pass while a DC (direct current) is blocked.
Gautam
A motor travelling at 72km/m on sighting a stop sign applying the breaks such that under constant deaccelerate in the meters of 50 metres what is the magnitude of the accelerate
velocity can be 72 km/h in question. 72 km/h=20 m/s, v^2=2.a.x , 20^2=2.a.50, a=4 m/s^2.
Mehmet
A boat travels due east at a speed of 40meter per seconds across a river flowing due south at 30meter per seconds. what is the resultant speed of the boat
which has a higher temperature, 1cup of boiling water or 1teapot of boiling water which can transfer more heat 1cup of boiling water or 1 teapot of boiling water explain your . answer
I believe temperature being an intensive property does not change for any amount of boiling water whereas heat being an extensive property changes with amount/size of the system.
Someone
Scratch that
Someone
temperature for any amount of water to boil at ntp is 100⁰C (it is a state function and and intensive property) and it depends both will give same amount of heat because the surface available for heat transfer is greater in case of the kettle as well as the heat stored in it but if you talk.....
Someone
about the amount of heat stored in the system then in that case since the mass of water in the kettle is greater so more energy is required to raise the temperature b/c more molecules of water are present in the kettle
pratica A on solution of hydro chloric acid,B is a solution containing 0.5000 mole ofsodium chlorid per dm³,put A in the burret and titrate 20.00 or 25.00cm³ portion of B using melting orange as the indicator. record the deside of your burret tabulate the burret reading and calculate the average volume of acid used?
No. According to Isac Newtons law. this two bodies maybe you and the wall beside you.
Attracting depends on the mass och each body and distance between them.
Dlovan
Are you really asking if two bodies have to be charged to be influenced by Coulombs Law?
Specific heat capacity is a measure of the amount of energy required to raise the temperature of a substance by one degree Celsius (or Kelvin). It is measured in Joules per kilogram per degree Celsius (J/kg°C).
AI-Robot
specific heat capacity is the amount of energy needed to raise the temperature of a substance by one degree Celsius or kelvin
ROKEEB
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