A body of mass 5 kg resting on a smooth horizontal plane, is acted upon by force 6i + 2j, 5i + 4j and 4i – j. Calculate the:
(a) velocity of the body
(b) Magnitude of its velocity after 4s.
Explanation
(a) Resultant of the forces acting on the plane = (6i + 2j) + (5i + 4j) + (4i – j) = 15i + 5j
(F = frac{m Delta v}{t})
Resultant force = (frac{mv}{t} )
(15i + 5j = frac{5v}{t})
(v = frac{(15i + 5j). t}{5} = 3t i + t j)
(b) velocity after 4 seconds = (3(4) i + 4 j = 12 i + 4 j)
(therefore |12i + 4j| = sqrt{12^{2} + 4^{2}} = sqrt{144 + 16})
= (sqrt{160} )
= (4sqrt{10} m/s)