1@saurabh
if u1 and u2 are constant , that doesn't mean they are equal. the ans. that u got is correct if it was given u1 = u2 =u. but in this question u1 nd u2 are not equal.
FIND VELOCITY OF BLOCK AT THE MOMENT SHOWN IN FIGURE.
(speed u1 and u2 are constant. give your ans. with respect to coordinate system shown in figure)
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8 Answers
1
since by Pythagoras Theorem,
z2 = x2 + y2 ......................... (1)
Now
we know that velocity V = drdt
therefore when we differentiate eq. (1) with respect to t we get,
dz2dt = dx2dt + dy2dt
=> 2zdzdt = 2xdxdt + 2ydydt
=> 2zU2 = 0 + 2yV ...................(2)
dzdt = U2 because U2 velocity is along z zxis or z length.
dxdt = 0 because x length remains constant or it does not vary.
dydt = V because V velocity is along y axis or y length.
since U1 = U2 = U (BECAUSE U1 AND U2 ARE CONSTANT)
so from eq. (2)
2zU = 2yV
=> V = zy * U
=> V = Secθ * U ( zy = Secθ)
hence VELOCITY OF BLOCK = Usecθ Ans..............
1right ans. is -
\large v = \frac{u_{1}+u_{2}}{2cos\theta } \, \hat{i} + \frac{u_{2}- u_{1}}{2sin\theta }\hat{j}
11if u say that U1 and U2 are constant then velocity must be constant that means both velocities must have same exact value.
howmuch i knew i have already writen.
1@saurabh
don't forget about \theta, vel. will varry with \theta , though for a particular \theta it would be constant....
71Absolutely agree. The Velocities U1 and U2 are constant but that Doesn't mean they are Equal. Their difference will decide the angle of movement of the body and hence the net Velocity!