One football is kicked into the air with an initial vertical velocity of 44 feet per second. Another football is kicked it to the air with an initial vertical velocity of 40 feet per second.
a. Which football is in the air for more time?
b. Justify your answer to part (a).
The first ball
Since u only mentioned weight and no other forces, we r dealing with a conservative system. Meaning the magnitude of the velocity of the ball right before it hits the ground is equal to that of the initial velocity. Vector wise the velocity points in the opposite direction than the initial velocity. Therefore v=-c where c is the initial velocity.
We know that
Let upward direction be positive and therefore a=-g where g is the grav constant. Integrate knowing that at t=0 we have the initial velocity c and at a time t we have v=-c we can eventually write
So the bigger the initial velocity, the bigger the time.