what eqaution can i use to predict the range of a spring if fired horizontally...im given...?

Question

height of 0.70 m
pulled back distance of 0.10 m
mass of 7 g
velocity of .21 m/s

Answer 1

The spring does not achieve its max horizontal velocity V until it returns to its uncompressed state

Range = Vt
Time t depends on the height above the landing point
h=0.5gt^2
t= sqrt(2 h /g)
finally
Range = Vt=V sqrt(2 h /g)

Range = 0.21 sqrt(2 x 0.7/9.81)=
Range =0.08m or 8cm
(Note: These calculations are based on a spring that turns rigid as soon as it achieve max velocity V. In reality the motion is bit more complex and basically a damped oscillation.)

Answer 2

Calculate kinetic energy for: mass of 7 g, velocity of .21 m/s. Set that equal to (1/2) k [(0.10 m)^2] and solve for k