modified version of a well known question : newton's laws.

no reply....??

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..............

right ans. is -

\large v = \frac{u_{1}+u_{2}}{2cos\theta } \, \hat{i} + \frac{u_{2}- u_{1}}{2sin\theta }\hat{j}

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.

@saurabh

don't forget about \theta, vel. will varry with \theta , though for a particular \theta it would be constant....

C'mon guys, give it a try....

Absolutely 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!