Below is a sketch of the initial state of the situation described in this problem. Draw the most suitable set of coordinate axes for this problem. Note that even though you can choose the y=0y=0 level to be wherever you like, in most situations it is best to set the zero height to coincide with either the initial or final position, so that the calculations for the gravitational potential energy become easier. For this reason, in this particular problem place the origin of your coordinate axes on the black dot marking the performer's initial position. Draw only the positive portion of the coordinate axes. Draw the vectors starting at the black dot. The location and orientation of the vectors will be graded. The length of the vectors will not be graded.

This problem is incomplete, it says like this: The Great Sandini is a 60 kg circus performer who is shot from a cannon (actually a spring gun). You dont find many men of his caliber, so you help him design a new gun. This new gun has a very large spring with a very small mass and a force constant of 1100 N/m that will compress with a force of 4400 N. The inside of the gun barrel is coated with teflon, so the average friction force will be only 40 N during the 4 m his moves in the barrel. At what speed will he emerge from the end of the barrel, 2.5 m above his initial rest position?

The speed is 15.5 m/s, and the image shows the vector drawing.

Explanation:

For the calculation of the force that is due to the spring is equal to:

F = kx

Where

F = 4400 N

k = 1100 N/m

x = F/k = 4400/1100 = 4 m

For the calculation of the total energy is equal to:

[tex]\frac{1}{2} kx^{2} =\frac{1}{2}mv^{2} +mgh+Fx\\v=\sqrt{\frac{2}{m} (\frac{1}{2}kx^{2} -mgh-Fx) }[/tex]

Where

m = 60 kg

h = 2.5 m

Replacing:

[tex]v=\sqrt{\frac{2}{60}(\frac{1}{2}*1100*4^{2}-60*9.8*2.5-(40*4)) } =15.5m/s[/tex]