Acceleration

Once the football has left the throwers, it is a projectile, which means that it is not accelerating forward. The only time the ball is accelerating forward is when it is in contact with the throwers hand, because during this time there is an unbalanced force acting on it (see Newton’s Second Law). When a force is applied to the back of the ball, it is considered an unbalanced force because there is no force pushing back at it the other way and causing it to remain at a constant velocity, so it accelerates. After that, there is nothing pushing it forwards or backwards, since air resistance was minimal, we know that it is no longer being accelerated. If the football were starting at rest, we could use just one calculation to figure out its acceleration, but in this case, the football had and applied force onto it, so we will need to find the horizontal and vertical components of the acceleration first, in order to find the actual acceleration.

After finding the horizontal acceleration I must now find the vertical acceleration. Now I can use Pythagorean theorem to solve for the acted acceleration caused by the throwers hand: I subed in the values that I got for horizontal acceleration and vertical accleration to find the acceleration of the throwers hand. I also used the values that i got for horizontal and vertical acceleration to find the angle of the cockback.

To find the vertical acceleration I used the final vertical velocity and initial vertical velocity (see Velocity and Components) and, the time it took for the football to reach the maximum height. After finding the vertical acceleration I used that value and the horizontal acceleration (0m/s² because the football only accelerates vertically, and it travles with a uniform motion horizontally) to solve for the actual acceleration. I can see that the that acceleration occurs because the football starts to move. If the football was to not accelerate, it would have to fall straight to the ground, but since it started to move forward, we know acceleration occurred.

Therefore the accleration of the football is 19.6m/s² (30⁰ above the horizontal).

Quaterback Colin Kaepernick of the San Francisco 49ers throwing a 30 yard pass.