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

Two particles having position vectors vec(r )_(1) = ( 3 hat(i) + 5 hat(j)) meters and vec( r)_(2) = (- 5 hat(i) - 3 hat(j)) metres are moving with velocities vec(v)_(1) = ( 4 hat(i) + 3 hat(j)) m//s and vec(v)_(2) = (alpha hat(i) + 7 hat(j)) m//s . If they collide after 2 s , the value of alpha is

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 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

An electron is moving with an initial velocity vec(V) = v_(0) hat(i) and is in a magnetic field vec(B) = B_(0)hat(j) . Then its de Broglie wavelength

An alpha particle moving with a velocity vec(v)_(1)=2hat(i)m//s is a uniform magnetic field experiences a force vec(F)_(1)=-4e(hat(j)-hat(k))N . When the particle moves with a velocity vec(v)_(2)=hat(j)m//s , then the force experienced by it is vec(F)_(2)=2e(hat(i)-hat(k))N . The magnetic induction vec(B) at that point is :

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

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 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) .