Finding time a ball is in the air

[mcryder16]

Homework Statement

A student standing on the ground throws a ball straight up. The ball leaves the student's hand with a speed of 15.44 m/s when the hand is 1.61 m above the ground. How long is the ball in the air before it hits the ground? (The student moves her hand out of the way.)

Homework Equations

I need help starting this problem

The Attempt at a Solution

 

[LowlyPion]

Homework Statement

A student standing on the ground throws a ball straight up. The ball leaves the student's hand with a speed of 15.44 m/s when the hand is 1.61 m above the ground. How long is the ball in the air before it hits the ground? (The student moves her hand out of the way.)

Homework Equations

I need help starting this problem

The Attempt at a Solution

See:
https://www.physicsforums.com/showpost.php?p=905663&postcount=2

 

[fallen186]

v_{f}=v_{o}+at
0m/s = 15.44 m/s +(-9.81m/s^2)*t
t = 1.574 s

v_{f}^2=v_{o}^2+2a*x
0 = 15.44^2m/s + 2 *(-9.81m/s^2) * x
x = 12.15 m
This is how high the ball travels from the hand.

-------------When the ball is returning to earth-----------
x = x_{0} +v_{0}t+\frac{1}{2}at^{2}
x = 12.15m + 1.61m = 13.76m
13.76m = 0m + 0m/s*t + \frac{1}{2} * 9.81m/s^2*t^2
27.52 = 9.81m/s^2*t^2
2.805 = t^2

t = 1.675 s

t_{total} = t_{ascent} +t_{decend}

t_{total} = 1.975s + 1.574 s

t_{total} = 3.549s