The footballer threw the ball vertically up 5 meters. Did the ball fly faster up or down?
h = 5 m. g = 9.8 m / s ^ 2. V = 0 m / s. top -? tdown -?
1) Let the footballer throw the ball up with the initial velocity V0. The body moves upward only under the action of gravity with the acceleration of gravity g, which is directed downward. The lift height is determined by the formula: h = (V ^ 2 – V0 ^ 2) / 2 * g. Since V = 0 m / s, the formula will take the form: h = – V0 ^ 2/2 * g. The sign “-” means that the speed and acceleration are oppositely directed, the body is braked. V0 = √ (2 * g * h). V0 = √ (2 * 9.8 m / s ^ 2 * 5 m) = 9.89 m / s. Rise time t up = V0 / g. tup = 9.89 m / s / 9.8 m / s ^ 2 = 1 s. 2) When moving down, the body also moves with an acceleration of gravity g and travels a path h = 5 m. The speed of the ball when hitting the ground will be expressed by the formula V = √ (2 * g * h). V = √ (2 * 9.8 m / s ^ 2 * 5 m) = 9.89 m / s. The time for the ball to drop tlow = V / g. tlow = 9.89 m / s / 9.8 m / s ^ 2 = 1 s.
Answer: the ball moves up and down for the same time tup = tlow = 1 s.