Projectile Motion in Combination with Energy Problem

[Bound]

Homework Statement

A toy rifle shoots a spring of mass 0.008kg and with a spring constant of 350 N/m. You wish to hit a target horizontally a distance of 15m away by pointing the rifle 45^o above the horizontal. How far should you extend the spring in order to reach the target?

Homework Equations

E = 1/2(k)(x)²
F = kx
KE = 1/2(m)(v)²
Any relevant kinematics formulae.

The Attempt at a Solution

Normally for questions like this I would equate potential spring energy to the kinetic energy, but here I am missing a velocity as well as the spring compression length so I am a little lost.

 

[Andrew Mason]

Homework Statement

A toy rifle shoots a spring of mass 0.008kg and with a spring constant of 350 N/m. You wish to hit a target horizontally a distance of 15m away by pointing the rifle 45^o above the horizontal. How far should you extend the spring in order to reach the target?

Homework Equations

E = 1/2(k)(x)²
F = kx
KE = 1/2(m)(v)²
Any relevant kinematics formulae.

The Attempt at a Solution

Normally for questions like this I would equate potential spring energy to the kinetic energy, but here I am missing a velocity as well as the spring compression length so I am a little lost.

Use the formula for horizontal range for projectile motion letting sin2θ = 1 and R = 15 m. to determine the initial velocity v that is needed. From that you can work out the kinetic energy and, therefore, the potential energy of the spring.

AM