Projectile Motion of a Grasshopper Problem

[maff is tuff]

Homework Statement

A grasshopper leaps into the air from the edge of a vertical cliff, as shown in the figure below.

Use information from the figure to find a) the initial speed of the grasshopper and b) the height of the cliff.

Homework Equations

v=v0 + at

x = x0 + v0t + 1/2(at^2)

v^2 = v0^2 + 2a(x-x0)

The Attempt at a Solution

I think I am missing something big because I'm not even getting close. I keep getting a negative under a radical. Can you please tell me what I am doing wrong or point me in the right direction? The diagram and my attempt is attached below. Thanks for the help:)

 

[ehild]

You are right that voy =gt where t is the time the grasshopper reaches the maximum height. But you substituted -gt for voy in the equation for the displacement.

ehild

 

[maff is tuff]

Doesn't gt have to be negative? Because gravity is downward and my initial velocity is upward so g has to be negative. right?

 

[ehild]

Gravity is negative, but g=9.8 m/s², and the acceleration is -g. But voy is positive (upward) voy=gt=9.8t

ehild