Solution

Football and balloon behave differently. Therefore we examine them separately.

Firstly we look at the football.

The football is inert and does not change its state of movement as long as there is no external force acting on it. For the reason that it is not connected firmly with the car the brake force is not transferred to it. So it retains the state of movement it was in before braking. Due to the fact that the football executed a linearly uniform movement before braking, just like the car and retains this movement now, it keeps on moving linearly. So the football flies forward in the direction of the front window.

You can watch the same behaviour with the ball in the video.