Calculating Potential Energy of a Bow + Projectile calculations

[xxshabsxx]

Homework Statement

I have a physics lad research that's due tomorrow, the overall process is to work out how much potential energy will be stored in a bow, and the efficiency of the bow.

First of all, I have a graph, with the plots Force Vs. Displacement (of a weight 'm' on a string). We are not given 'k', so how would I work out the potential energy of the bow without it?

Secondly, we are to work out the initial velocity of a bow (and therefore working out the kinetic energy) when fired at an angle of 45 Degrees. We are only given the mass of the arrow (6.5g), the horizontal displacement (1.85m) and the vertical displacement (0.65cm).

If I used the formula u=x/t, how would I find 't' given only the things above?

Homework Equations

PE=1/2kv^2
KE=1/2mv^2
u=xt

The Attempt at a Solution

I've got a lot of working out on page, but none of it helps. I'm use completely lost on what to do.

I'm not that great of physics, so try and keep it as uncomplicated as you can.

Thanks in advance!

 

[Zubeen]

First, you must be knowing about the formula F= k*x, so we have k=F/x.
in case of the plot with you, the ratio F/x is the slope of the straight line of the plot.
so take any force and corresponding displacement (if the straight line passes through 0 ) and get k as above.
then, let v be the initial velocity then, the vertical velocity will be v*sin(45) , this vertical velocity will be 0 at the highest point so from v=u + at, we have
0=v*sin(45) - gt => t=v*sin(45)/g
now we have for horizontal displacement, with initial velocity v*cos(45),
x= ut => 1.85=v²/2g
so v² = 1.85*2g
and then you can get K.E.
Zubeen