Ball Launched from spring gun (max height)

[jti3066]

Homework Statement

A ball of mass m is launched at an angle theta from a spring gun of length D. The lower end of the gun, where the spring is attatched, is at ground level. The spring has spring constant k and an unstretched length D. Before launch, the spring is compressed to a length d.

Determine the maximum height h above the ground the ball reaches.

Homework Equations

(k(x^2)/2)=mgh

?? x = mgcos(theta)

The Attempt at a Solution

Plugging in "x" I get: h=(k(mgcos(theta))^2)/2mg

Is this correct? If not please explain in detail and provide the steps and solution. TIA.

 

[Doc Al]

(k(x^2)/2)=mgh

Here x is a velocity. You can use conservation of energy to find the additional height reached after the ball leaves the gun, if x is the vertical component of the speed at that point. Note that h will not be the height above the ground.

?? x = mgcos(theta)

You can't set a velocity (x) equal to a force.

The Attempt at a Solution

Plugging in "x" I get: h=(k(mgcos(theta))^2)/2mg

Is this correct?

No. Note that you haven't even used the spring constant or the amount the spring was compressed.

Try to solve it in two steps: Find the speed of the ball as it leaves the gun. Then find the height that it reaches after it becomes a projectile.

 

[jti3066]

Well then I guess I have no idea what I'm doing then...A little more help please

K_i + U_i + S_i = K_f + U_f + S_f

K = .5mv^2

U = mgh

S = .5kx^2

What is the muzzle velocity?

How to find the height that it reaches?

 

[Doc Al]

K_i + U_i + S_i = K_f + U_f + S_f

K = .5mv^2

U = mgh

S = .5kx^2

What is the muzzle velocity?

To find the muzzle velocity, use conservation of energy as you outlined above. Hint: What's the change in height of the ball as it travels through the gun?

How to find the height that it reaches?

Once the ball leaves the gun it's a projectile. Solve that part like any other projectile motion problem.

 

[jti3066]

Could someone please solve the problem for me...BTW this is NOT a homework problem...It is a final test review problem...I learn differently than most...By looking at the steps involved in solving the problem along with the answer I can use deductive reasoning as to why those methods were used...TIA