Homework StatementA Certain potato "canon" consists of a 1.2 m tube with a thin platform inside. The Platform has a negligible mass and is attached to a spring. The spring is 20 cm long when relaxed, and the spring is compressed to a final length of 5 cm when ready to launch a potato. A potato is placed in the tube, touching the platform. This particular potato has a mass of 375 g and a length of 10cm. There is an average frictional force of 2.8 N between the potato and the inside of the tube. When the spring is released the potato is launched.
1) What is the value of the spring constant such that the potato has a range of 30 cm when fired in the orientation of 40 degrees with respect to the horizontal plane.
Force of spring = (k)(Δx)
The Attempt at a Solution
I thought about using the formula R = (v^2(initial) * sin2θ)/g
where R is the range. But I'm not exactly sure if using that formula would be correct.
Would that v(initial) be the velocity that leaves the launcher and from there we need to find out what spring constant would give that amount of launch velocity?
I don't know where to begin. Please help.
Does the potato have to end on the same height to use the above formula?