4. A particle of mass \( m=5 kg \), initially at rest at \( x=0 \) and \( y=0 \) is acted upon by two forces \( \vec{F}_{1} \) and \( \vec{F}_{2} \). The force \( \vec{F}_{1} \) is shown in the diagram. Note that \( \sin \theta=4 / 5 \). The net acceleration of the particle is \( \vec{a}=12 \hat{i} m / s ^{2}, \vec{a} \) is shown in the diagram.
(a) What is the force \( \overrightarrow{ F }_{2} \) ? Show graphically \( \overrightarrow{ F }_{2} \) on the diagram.
(b) What is the position vector of the particle at \( t=10 s \) ?
(c) What is the velocity of the particle at \( t=10 s \) ?
(d) What additional force \( \overrightarrow{ F }_{3} \) would be required to make the acceleration \( \overrightarrow{ a }=0 \) ?
Give the magnitude and the direction of \( \overrightarrow{ F }_{3} \) or express \( \overrightarrow{ F }_{3} \) in terms of its components.