A Discussion On Compressed Springs And Spring Constants

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Spring Question-Compressed Spring
In a physics lab experiment, a compressed spring launches a 22g metal ball at a 35 degree angle. Compressing the spring 19cm causes the ball to hit the floor 2.0m below the point at which it leaves the spring after traveling 5.4m horizontally.
What is the spring constant?
k = __________________ N/m

Let the spring constant be K and the velocity of the ball just after it released is v.
As the elastic potential energy stored in the spring compressed by L is given by
U = ½ K L2
Using law of conservation of mechanical energy the velocity of projection v is given by
Gain in kinetic energy = loss in elastic potential energy
Or
Or --------------------- (1)
Now for a projectile motion using the equation of trajectory (point of projection as origin and upward direction positive) is written as

Here  is the angle of projection and (x, y) is the coordinates of any point on the trajectory.
Now in our case as (x, y) = (5.4 m, - 2.0 m) and  = 35 deg, substituting in above equation of trajectory we get

Or
Or
Gives
Substituting this in equation (1) with other values we get

Or
Thus the spring constant of the spring is 22 N/m.

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