Projectile Motion of a grasshopper off a cliff

[Todd88]

Homework Statement

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

Homework Equations

Use information from the figure to find the height of the cliff.

The Attempt at a Solution

The first question was to find the initial speed of the grasshopper. I found this to be 1.5m/s.

I have tried using this equation to get the height of the cliff but it isn't right:

h = ut + (1/2)gt² where u is the initial velocity. Any help is greatly appreciated.

 

[Delphi51]

How did you get the 1.5 m/s?
You must separate the vertical and horizontal motion - they are independent.
Make two headings "horizontal" and "vertical". Write x = vt under the horizontal heading and the accelerated motion formulas under the vertical heading. Fill in all the numbers you have. Note that while you don't know the initial Vx or Vy, you do know their ratio, so enter Vx as an unknown and then Vy as Vx times a tangent. If you have only one unknown in one of the formulas, begin with that! If not, you'll have to use 2 or 3 of them and solve as a system of equations.

Show your equations here if you would like more help!

 

[Todd88]

Well to get the components of the velocity it is just 1.5sin(50) and 1.5cos(50) so can I just use the y-component and plug that into the formula to find the total distance traveled in the y direction?

 

[Delphi51]

Okay, I found the 1.5 too. Tricky calc!
I think you will have to use the horizontal distance first - it matters. Use it to find the time of flight and then use the vertical part to find the vertical distance.

 

[Todd88]

Okay I got the total time to be 1.0993 s. I used this :

t = 1.06 m / (1.5cos 50)

Not sure where to go to from here...

 

[Todd88]

Bah, I got it. Just use that time, then the y-component and use the equation:

x = x0 + V0xt + 1/2axt^2

Simple...Thanks a lot for your help!