Projectile Motion 2D - Spring Launched

[reaganks]

Projectile Motion 2D -- Spring Launched

There is this ball launched from a slingshot. Given the mass is 0.9 kg at the angle 60° to the horizontal, with k=750 N/m and is stretched by length l = 0.6 m. The ball is shot 1 m above the ground. (g=10 m/s²).

The questions are to derive the equation describing the velocity and trajectory with the aerodynamic drag negligible.

My approach is first to find the acceleration in x and y direction.
F = k.x = 750x0.6 = 450 N
Fx = F cos 60 = 389.71 N, Fy = F sin 60 = 225 N

Horizontal:
Fx = m*a_x
a_x = 250 m/s²

Vertical:
Fy - mg = m*a_y
a_y = 423.01 m/s²

Then I find the Velocity
Vx = Vox + 250t
Vy = Voy + (423.01-10)t = Voy + 413.01t

My problem is now finding the initial Velocity Vo. I was thinking of using Energy principal but then I am stuck with the velocity of the ball at certain point, thus, I was not able to solve it.

 

[dirk_mec1]

The initial velocity is zero.

 

[PhysicoRaj]

The initial velocity is zero.

There is this ball launched from a slingshot.
with k=750 N/m and is stretched by length l = 0.6 m.

So the initial velocity will be nonzero.

 

[dirk_mec1]

Oh yes that's right my bad. Use an energy equation 1/2kx^2 = 1/2 mv(0)^2.