Ship A moving with velocity `vec(V_(1)) = 30 hat(i) + 50 hat(j)` from position (0, 0) and ship `B` moving with velocity `vec(V_(2)) = - 10 hat(i)` from position (80, 150). The time for minimum separation is : (A) 2.6 (B) 2.2 (C) 2.4 (D) None

A portion is fired from origin with velocity vec(v) = v_(0) hat(j)+ v_(0) hat(k) in a uniform magnetic field vec(B) = B_(0) hat(j) . In the subsequent motion of the proton

A conductor AB of length l moves in x y plane with velocity vec(v) = v_(0)(hat(i)-hat(j)) . A magnetic field vec(B) = B_(0) (hat(i) + hat(j)) exists in the region. The induced emf is

In a region of space , suppose there exists a uniform electric field vec(E ) = 10 hat(i) ( V /m) . If a positive charge moves with a velocity vec(v ) = -2 hat(j) , its potential energy

A particle travels so that its acceleration is given by vec(a)=5 cos t hat(i)-3 sin t hat(j) . If the particle is located at (-3, 2) at time t=0 and is moving with a velocity given by (-3hat(i)+2hat(j)) . Find (i) The velocity [vec(v)=int vec(a).dt] at time t and (ii) The position vector [vec(r)=int vec(v).dt] of the particle at time t (t gt 0) .

A particle is moving with a constant acceleration vec(a) = hat(i) - 2 hat(j) m//s^(2) and instantaneous velocity vec(v) = hat(i) + 2 hat(j) + 2 hat(k) m//s then rate of change of speed of particle 1 second after this instant will be :

If vec(F ) = hat(i) +2 hat(j) + hat(k) and vec(V) = 4hat(i) - hat(j) + 7hat(k) what is vec(F) . vec(v) ?

A magnetic field vec(B) = B_(0)hat(j) , exists in the region a ltxlt2a , and vec(B) = -B_(0) hat(j) , in the region 2a lt xlt 3a , where B_(0) is a positive constant . A positive point charge moving with a velocity vec(v) = v_(0) hat (i) , where v_(0) is a positive constant , enters the magnetic field at x= a . The trajectory of the charge in this region can be like

If vec(a)= 3hat(i) + hat(j) + 2hat(k) and vec(b)= 2hat(i)-2hat(j) + 4hat(k) , then the magnitude of vec(b) xx vec(a) is

A charged particle moves with velocity vec v = a hat i + d hat j in a magnetic field vec B = A hat i + D hat j. The force acting on the particle has magnitude F. Then,

A charged particle moves with velocity vec v = a hat i + d hat j in a magnetic field vec B = A hat i + D hat j. The force acting on the particle has magnitude F. Then,