It's hard to tell what what this problem looks like from your description. Also, conservation of momentum does not apply if you have the energy being transferred from the spring to the block and plank. Anyway, there's some good Physics Solvers with Conversions at http://bluesolver.com, if that...
You need to calculate the motion in the horizontal and vertical directions. This is assuming you shot the projectile vertically from the height indicated.
x = v0*t
y = -(1/2)*g*t^2
So you would use the vertical equation to calculate time:
t = sqrt(2 * y / g)
t = sqrt(2 * 2.98 / 9.8)...
For the first problem:
Force A Horizontal = 35,600 * sin(22)
Force B Horizontal = ForceB * sin(39)
Force B = 35,600*sin(22)/sin(39)
For the second problem:
I think you can just add the accelerations to get 5.74m/s^2. Might want to check that part.
Next calculate the force you'll...
I wouldn't worry about tension or balancing the forces if the question does not ask for it. I think your equations look correct. Here's how I think you should approach the problem.
From the definition of linear density:
rho = dm/dx.
Therefore you could substitute dm in both equations...