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..............
1
Hodge Conjecture
·2010-08-23 00:22:57
right ans. is -
\large v = \frac{u_{1}+u_{2}}{2cos\theta } \, \hat{i} + \frac{u_{2}- u_{1}}{2sin\theta }\hat{j}
1
Hodge Conjecture
·2010-08-23 00:26:37
@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.
1
saurabh singhal
·2010-08-23 06:59:50
if 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
Hodge Conjecture
·2010-08-23 10:16:00
@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!
