5.66 seconds from when the rock was thrown.
First construct an expression to represent the distance from the water to the rock. First account for the starting distance.
d = 43 + ?
Now add in the distance based upon the initial velocity
d = 43 + 21t + ?
Now add in the acceleration due to gravity
d = 43 + 21t - 0.5at^2
Now substitute the known values into the formula.
5 = 43 + 21t - 0.5*9.8*t^2
Subtract 5 from both sides and perform the multiplication
0 = 38 + 21t - 4.9t^2
We now have a quadratic function with a=-4.9, b=21, c=38.
Using the Quadratic formula, we can find the solutions at
t = 5.66 and t=-1.37
Since the negative time doesn't make sense, the correct value will be t = 5.66 seconds.
