A boy throws a stone with an initial velocity of 14.6 m/s and it returns to his hand in 3 seconds. What maximum height does the stone reach?
You have been given more information than you need to solve the problem. The initial velocity Vo is enough to compute the answer.
It rises until the potential energy equals the initial kinetic energy.
M g H = (1/2)M Vo^2
H = Vo^2/(2 g) is the maximum heigh
= 10.9 m
If you use the time in the air (3 s) to get the answer,
1.5 seconds is the time spent rising.
H = (1/2)*9.8*(1.5)^2 = 11.0 m