- #1

reaganks

- 1

- 0

**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/s

^{2}).

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/s

^{2}

Vertical:

Fy - mg = m*a

_{y}

a

_{y}= 423.01 m/s

^{2}

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.