Respuesta :
Answer:
It will take 2.64 s for Felix's penny to hit the ground.
Initial velocity of Oscar's penny is 7.27 m/s or 23.85 ft/s
Step-by-step explanation:
Given:
Height of the tower is, [tex]h=112\ ft[/tex]
Felix drops the penny while Oscar throws his penny.
Time taken by Oscar's penny to reach ground is, [tex]t_o=2\ s[/tex]
Now, as Oscar throws his penny, there will be some initial velocity of his penny. Let the initial velocity of his penny be [tex]u_o[/tex].
As the penny is falling vertically, acceleration of the penny is due to gravity and is equal to -9.8 m/s².
Now, displacement of the penny is equal to the height of the tower = -112 ft = -34.14 m (1 ft = 0.3048 m)
Using equation of motion,
[tex]y=u_ot+\frac{1}{2}at_o^2\\\\-34.14=2u_o-\frac{1}{2}\times9.8\times 2^2\\\\-34.14=2u_o-19.6\\\\2u_o=-34.14+19.6\\\\2u_o=-14.54\\\\u_o=\frac{-14.54}{2}=-7.27\ m/s[/tex]
Now, 1 m/s = 3.28 ft/s
So, 7.27 m/s = [tex]7.27\times 3.28 = 23.85\ ft/s[/tex]
Therefore, the initial velocity of Oscar's penny is 7.27 m/s or 23.85 ft/s in the downward direction.
Now, Felix drops the penny. So, initial velocity of Felix's penny is 0 m/s.
Displacement of the penny is same and equal to -112 ft = -34.14 m
Using the same equation of motion,
[tex]y=ut+\frac{1}{2}at^2\\\\-34.14=0-\frac{1}{2}\times9.8\times t^2\\\\-34.14=-4.9t^2\\\\t^2=\frac{-34.14}{-4.9}\\\\t=\sqrt{\frac{-34.14}{-4.9}}\\\\ t=2.64\ s[/tex]
Therefore, time taken by Felix's penny to reach ground is 2.64 s.
