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(A) The motion of the sphere is analogous to projectile motion where the acceleration is constant in the $x$-direction.Given: Mass $m = 500 \ g = 0.5

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(A) The motion of the sphere is analogous to projectile motion where the acceleration is constant in the $x$-direction.Given: Mass $m = 500 \ g = 0.5 \ kg$,Force $F_x = 0.9 \ N$,Initial velocity $v = 3 \ m/s$ at an angle $	heta = 30^{\circ}$ with the $y$-axis.The acceleration in the $x$-direction is $a_x = \frac{F_x}{m} = \frac{0.9 \ N}{0.5 \ kg} = 1.8 \ m/s^2$.The initial velocity component in the $x$-direction is $u_x = v \sin(30^{\circ}) = 3 	imes 0.5 = 1.5 \ m/s$.The sphere crosses the $y$-axis again when its displacement in the $x$-direction becomes zero,i.e.,$s_x = 0$.Using the equation of motion $s_x = u_x t + \frac{1}{2} a_x t^2$:$0 = (1.5)t + \frac{1}{2} (-1.8) t^2$ (Note: The force acts in the $+x$ direction,but the initial velocity component is in the $-x$ direction,so acceleration is opposite to initial velocity).$0 = 1.5 t - 0.9 t^2$$0.9 t^2 = 1.5 t$$t = \frac{1.5}{0.9} = \frac{15}{9} = \frac{5}{3} \approx 1.66 \ \sec$.

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