A \(0.45-\mathrm{kg}\) soccer ball is kicked at an angle \(\theta\) above the ground with initial speed \(v_{\mathrm{i}}\).

(a) Determine the height of the ball as a function of the horizontal distance it travels down the field.

(b) For \(\theta=30^{\circ}\), what initial speed must the ball have in order to land \(48 \mathrm{~m}\) from where it is kicked?

(c) If the foot is in contact with the ball for \(0.15 \mathrm{~s}\), what is the average force exerted by the foot on the ball?