The angle between and is
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Given,
As we know that
where is the angle between and
Which one of the following statements is true?
A scalar quantity is the one that is conserved in a process
A scalar quantity is the one that can never take negative values
A scalar quantity is the one that does not vary from one point to another in space
A scalar quantity has the same value for observers with different orientation of the axes
A scalar quantity does not depend on direction so it has the same value for observers with different orientations of the axes.
If and , Which of the following is correct?
and are positive while and are negative
and are positive while is negative
and are all positive
From the diagram,
As is in the first quadrant, so both components and . will be positive.
For , as it is in positive -direction and located downward so -component will be positive and component will be negative.
The component of a vector along -axis will have maximum value if
is along positive -axis
makes an angle of with the -axis
is along negative -axis
Hence, and are positive but is negative.Let makes an angle with positive -axis component of along -axis.
is maximum of
.
Hence the vector has maximum value along positive -axis.
The horizontal range of a projectile fired at an angle of is . If it is fired with the same speed at an angle of , its range will be
Consider, projectile is fired at an angle .
According to question,
and
Range,
Now,
Consider the quantities, pressure, power, energy, impulse, gravitational potential, electrical charge, temperature, area. Out of these, the only vector quantities are :
impulse, pressure and area
impulse and area
area and gravitational potential
impulse and pressure
As we know that;
Impulse,
where is force, is time duration and is change in momentum. As is a vector quantity, hence impulse is also a vector quantity. Sometimes area can also be treated as vector.
In a two dimensional motion, instantaneous speed is a positive constant. Then, which of the following are necessarily true?
The average velocity is not zero at any time
Average acceleration must always vanish
Displacements in equal time intervals are equal
Equal path lengths are traversed in equal intervals
As speed is a scalar quantity, hence it will be related with path length (scalar quantity) only:
Hence, Speed
So, total distance travelled Path length
speed time taken
Hence, path length which is scalar and traversed in equal intervals.
The acceleration of the particle is zero
The acceleration of the particle is bounded
The acceleration of the particle is necessarily in the plane of motion
The particle must be undergoing a uniform circular motion
As given that in two dimensional motion the instanteous speed is positive constant and we know that acceleration is rate of change of velocity or instantaneous speed and hence it will also be in the plane of motion.
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