Answer
(a) F = 19.0 N and $a = 1.03~m/s^2$
(b) F = 14.0 N and $a = 0.757~m/s^2$
Work Step by Step
(a) $F = \sqrt{F_1^2 + F_2^2}$
$F = \sqrt{(10.2 ~N)^2+(16.0 ~N)^2} = 19.0 ~N$
$ma = F$
$a = \frac{F}{m} = \frac{19.0 ~N}{18.5 ~kg} = 1.03~m/s^2$
(b) $F_x = F_{1x} = 10.2 ~cos(30^{\circ}) ~N = 8.83 ~N$
$F_y = F_{1y} + F_2 = -10.2 ~sin(30) ~N + 16.0 ~N = 10.9 ~N$
$F = \sqrt{F_x^2 + F_y^2}$
$F = \sqrt{(8.83 ~N)^2+(10.9 ~N)^2} = 14.0 ~N$
$ma = F$
$a = \frac{F}{m} = \frac{14.0 ~N}{18.5 ~kg} = 0.757~m/s^2$
