How do I calculate the spring constant with given projectile motion data?

[senseandsanity]

A spring clamped to the table is used to shoot a 20 g ball at a 30 degree angle. When the spring is compressed 20 cm, the ball travels horizontally 5.0 m and lands 1.5 m below the point at which it left the spring. What is the spring constant?

I know how to find the spring constant once I know the velocity but I'm stuck on the velocity.

 

[cyby]

You are able to calculate the velocity. You can actually figure it out using kinematics.

But I have a question... now, when the ball is shot, it is shot off at a 30 degree angle, right? So the ball doesn't just travel horizontally...

 

[marlon]

Using conservation of total energy you can calculate the spring constant as a function of the velocity, but then i guess you already knew that. Keep in mind here that you also need to include gravity because this is a two-dimensional-motion.

The velocity value you acguire from these calculations is the initial velocity $$v_{initial}$$.

Then just calculate the horizontal and vertical velocity and position of an object with certain initial velocity, which moves under the influence of gravity...These formula's are to be found in your textbooks, but using your brain you can also derive them:

F=-mg *e _y

$$v_x = v_{0x}$$
$$x-x_0 = v_{0x} * t$$
$$v_y = v_{0y} -gt$$
$$y-y_0 = v_{0y}*t -gt^2/2$$

good luck

marlon