To determine the initial velocity of the stone, we can use the equation of motion for vertical motion under constant acceleration:
h = h0 + v0t - (1/2)gt^2
Where: h is the final height (zero in this case, as the stone returns to its initial position), h0 is the initial height (also zero, since the stone starts at ground level), v0 is the initial velocity we want to find, t is the time of flight (4 seconds in this case), and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Since the stone returns to its initial position, the final height (h) is zero. Also, the initial height (h0) is zero since the stone starts at ground level. Plugging in these values into the equation, we get:
0 = 0 + v0(4) - (1/2)(9.8)(4)^2
0 = 4v0 - 78.4
Simplifying the equation:
4v0 = 78.4
v0 = 78.4 / 4
v0 = 19.6 m/s
Therefore, the initial velocity of the stone is 19.6 m/s when launched straight up by the sling shot.