Answer:
14.7 m/s
Explanation:
Since the motion of the ball is a uniformly accelerated motion, we can find the initial speed by using the following suvat equation:
[tex]s=ut+\frac{1}{2}at^2[/tex]
where
s is the vertical displacement
u is the initial velocity
t is the time
a is the acceleration
In this problem, we have:
s = 0 (because at the end of the motion, the ball returns to its original position)
u = ?
[tex]a=g=-9.8 m/s^2[/tex] is the acceleration of gravity (negative because it is downward)
[tex]t = 3 s[/tex] is the total time of flight
Solving for u, we find the initial velocity of the ball:
[tex]0=ut+\frac{1}{2}at^2\\u=-\frac{1}{2}at=-\frac{1}{2}(-9.8)(3)=14.7 m/s[/tex]
