Question

A soccer ball kicked on a level field has an initial vertical velocity component of 15.0 meters per second. Assuming the ball lands at the same height from which it was kicked, what is the total time the ball is in the air? [Neglect friction.]

Answer 1

Gravity will slow the upward component of the velocity of the ball until it reaches zero. The time it takes for this will be half the total travel time of the ball (since it has to come back down the same distance). We have:\[v_f=v_i-g t\]final velocity i zero, initial velocity is 15m/s and g=9.81 m/s^2. So we solve for time:\[t=\frac{15}{9.81}=1.53s\]This represent half the total time of the trip, so we multiply by two and get:\[t_{total}=3.06s\]