A soccer player kicks a ball with a speed of 30 m/s at an angle of 10. How long does the ball stay in the air?



4 years ago Comment

"10" is not a very satisfying description of an angle.
I'll assume it's 10 degrees, and that it's the angle of the initial trajectory
above the horizontal.

The vertical component of the ball's speed is 30 sin(10°) = 5.209 meters per second.

The acceleration of gravity is 9.8 meters per second² downward.

The ball continues to rise for 9.8/5.209 = 1.881 seconds after the kick.
At that time, it reaches the peak of its arc, and if nobody else has contacted it yet,
it begins to fall, and takes the same length of time to return to the ground whence
it was kicked.

So the time between the kick and return to the ground is (2 x 1.881) = 3.763 seconds.

Note: As is customary and necessary at the high school level,
we assume no air resistance.