A student climbs to the top of the gym and drops a baseball to the ground below. A physics student standing nearby has a motion sensor and determines that the baseball hit the ground with a velocity of 17 m/s. if you ignore air resistance, how long was the baseball falling through the air?​

Respuesta :

Answer:

The baseball was falling during 1.733 seconds.

Explanation:

The baseball experimented a free fall, which is a particular case of uniformly accelerated motion, in which object is accelerated by gravity. In this case, we need to determine the time spent by the ball before hitting the ground ([tex]t[/tex]), measured in seconds, which is determined by the following kinematic formula:

[tex]t = \frac{v-v_{o}}{g}[/tex] (1)

Where:

[tex]v_{o}[/tex], [tex]v[/tex] - Initial and final speeds of the baseball, measured in meters per second.

[tex]g[/tex] - Gravitational acceleration, measured in meters per square second.

If we know that [tex]v_{o} = 0\,\frac{m}{s}[/tex], [tex]v = 17\,\frac{m}{s}[/tex] and [tex]g = 9.807\,\frac{m}{s^{2}}[/tex], then the time spent by the baseball is:

[tex]t = \frac{17\,\frac{m}{s}-0\,\frac{m}{s} }{9.807\,\frac{m}{s^{2}} }[/tex]

[tex]t = 1.733\,s[/tex]

The baseball was falling during 1.733 seconds.