Two children pull a third child on a tricycle by means of two ropes tied to the handlebars. The combined inertia of the child and tricycle is \(35 \mathrm{~kg}\). One child pulls with a constant force of \(100 \mathrm{~N}\) directed to the right of the straight-ahead direction at an angle of \(45^{\circ}\).

(a) If the second child pulls with a force of \(80 \mathrm{~N}\), at what angle to the left of the straight-ahead direction must he pull to make the tricycle move straight ahead? 

\((b)\) With the second child pulling at the angle you calculated in part \(a\), what is the acceleration of the tricycle?

(c) What is the work done on the tricycle by the two ropes if the children pull constantly like this while the tricycle moves \(2.0 \mathrm{~m}\) ?