You kick a soccer ball with a speed of 12 m/s at an angle of 21. how long does it take the ball to reach the top of its trajectory?

2.42 seconds

Assume that air resistance is negligible, use trigonometry to find the vertical component of the velocity by using trigonometry:

31⋅sin50=23.7

Where 31 ms−1 is the hypotenuse and by using sin to get the opposite component (vertical velocity) of the trajectory.

Now comes the use of the formula:
v = u + at
where v is the final velocity (0 ms−1), u is the initial velocity (31 ms−1 ), a is the acceleration of gravity (9.81 ms−2) and t is the time it takes to arrive at the top of the trajectory.

By making t as the subject:

t=v−ua

You can calculate the value of t:

0−23.7−9.81=2.42 (to 3 significant figures)

Better way to see it:

0−(31⋅sin50)−9.81=2.421 (to 4 significant figures)

Note: You must remember that you are dealing with velocity, not speed . Since velocity is a vector quantity, you must select the direction at which values will be positive. In my example, I set my upward direction as the positive value while my downward vectors as negative value (a, acceleration, 9.81 ms−1).

t.                 w               e                 n                   t                 y                 c             h               a           r           a               c                 t             e             r             s        

answer: 0

explanation: im   14