Two forces (2i – 5j)N and (-3i + 4j)N act on a body of mass 5kg. Find in (ms^{-2}), the magnitude of the acceleration of the body.
-
A.
(frac{sqrt{2}}{5}) -
B.
(5sqrt{2}) -
C.
(2sqrt{5}) -
D.
(frac{5sqrt{2}}{2})
Correct Answer: Option A
Explanation
(F = F_{1} + F_{2})
((2i – 5j) + (-3i + 4j) = (-i – j))
(F = ma implies (-1, -1) = 5a)
(a = (-frac{1}{5}, -frac{1}{5}))
(|a| = sqrt{(frac{-1}{5})^2 + (frac{-1}{5})^2} = sqrt{2}{25})
(|a| = frac{sqrt{2}}{5} ms^{-2})