A particle of mass 2 kg is projected in the xy -plane with an initial velocity u = 4 i + 3 j ms ⁻¹ . It experiences a constant force F = -4 i - 8 j N . The time after which its velocity vector becomes perpendicular to its initial velocity vector is

Step-by-step solution

The initial velocity is u = 4 i + 3 j ms ⁻¹ . The acceleration of the particle is: a = F m = -4 i - 8 j 2 = -2 i - 4 j ms ⁻² The velocity of the particle at any time t is: v (t) = u + a t = (4 - 2t) i + (3 - 4t) j For the velocity to be perpendicular to the initial velocity, their dot product must be zero: v (t) u = 0 (4 - 2t)(4) + (3 - 4t)(3) = 0 16 - 8t + 9 - 12t = 0 25 - 20t = 0 t = 25 20 = 5 4 s Answer: 5 4 s