Question

A football is kicked from a tee at 12 m/s at 72° above the horizontal. What is the flight time of the football? __s

Answer 1

2.3 seconds    

Ignoring air resistance, the flight time is merely a function of gravity and vertical velocity. The vertical velocity will be the initial velocity multiplied by the sine of the angle above the horizon. So: 

 V = sin(72)*12 m/s 

 V = 0.951056516 * 12 m/s 

 V = 11.4126782 m/s   

 Gravitational acceleration is 9.8 m/s, so divide the vertical velocity by gravitational acceleration to get how long it takes for the ball to reach its apex. 

 11.4126782 m/s / 9.8 m/s^2 = 1.164559 s   

 And the old saying "What goes up, must come down" really applies here. And conveniently, it's also symmetric, in that the time it takes to fall will match the time it takes to reach its apex. So multiply the time by 2.  



1.164559 s * 2 = 2.329117999 s   

 Rounding the result to 2 significant figures gives 2.3 seconds.