What Happens to the Magnitude of a Vector When Rotated?

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When a vector is rotated, its magnitude remains unchanged regardless of the angle of rotation. In the first question, the vector's magnitude does not increase or decrease when it is rotated further counter-clockwise. For the second question, the direction of the vector can be determined by calculating the angle based on its components, Ex = +150 N/C and Ey = -100 N/C. The angle is found to be closest to +304°, indicating the vector's orientation in the coordinate system. Understanding these principles is crucial for solving physics problems related to vector rotation and components.
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hi everyone, i was doing my physics homework and i had problems in these 2 MC quesitons.

#1 A vector originally at a direction of 30°, when measured counter-clockwise with respect to the +x axis, is rotated a further 30° counter-clockwise.
The magnitude of the vector will ...

a.Increase by a factor of four
b.Increase by a factor of two
c.Remain the same
d.Decrease by a factor of two
e.Decrease by a factor of four

#2 The components of vector are Ex = +150 N/C and Ey = -100 N/C.
If we measure all angles with respect to the +x axis and counter-clockwise as the positive direction, the direction of is closest to:


a. -326°
b. -56°
c. -34°
d. +34°
e. +304°
 
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1) What do you think?

2) Draw the components.
 
1) draw a 30 degree, and 60 degree angle. but think about this: does your magnitude have anything to do with the changing of angles?
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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