Calculating spring constant of a spring loaded cannon

[alphaQ]

Homework Statement

if you wanted to build a spring launched cannon that will shoot you over a building that is 35 m high and 30 m wide, and the cannon is being shot at 60 degrees. If the cannon can be no more than 2 m long, what spring constant do you need in the spring to make this work? here is what I have been able to do, any feed back would be appreciated.

Homework Equations

^2= r/()
PE = KE
½ Fx = ½ mv^2
K = F / x

The Attempt at a Solution

to find the velocity I used:

v = sqrt((30* 9.8 m/s^2)/sin(60))
v = 18.425 m/s

Theoretically, humans can handle any velocity, it’s acceleration that we cannot handle well. A typical human can handle up to 5Gs of acceleration, that’s 49 ^2.

Since the maximum PE of the spring is the maximum KE of the mass PE = KE ½ Fx = ½ mv^2 Rearranging the formula, we get: = ^2/

F = ma = (70kg) (49m/s2) = 3430 N

KE = ½ mv2 = ½ (70kg) (18.425 m/s2) = 644.875 J

So, x = (644.875 J) / (½ ) (3430 N) x = 0.3760204082 m

We can now use x to solve for the spring constant

K = F / x

K = 3430N / 0.3760204082m + 2m(for the length of the cannon)

K = 1443.590294 N/m

is this K the right spring constant for this question?
[/B]

 

[haruspex]

v = sqrt((30* 9.8 m/s^2)/sin(60))

Not so fast: the building has a height and a width. You must clear it completely.
Draw a diagram.

 

[alphaQ]

Not so fast: the building has a height and a width. You must clear it completely.
Draw a diagram.

thats where i have the problem, i don't know how to incorporate the width and height into the equation

 

[haruspex]

thats where i have the problem, i don't know how to incorporate the width and height into the equation

You are looking for the minimum energy, so only just clearing the building.
If the launch is at speed v and distance x from the building, what equations can you write for just clearing it?
(Take the launch speed as being at ground level.)

 

[alphaQ]

You are looking for the minimum energy, so only just clearing the building.
If the launch is at speed v and distance x from the building, what equations can you write for just clearing it?
(Take the launch speed as being at ground level.)

i was thinking of getting the spring constant and then checking whether that constant would allow me to get over the height of the building

 

[haruspex]

i was thinking of getting the spring constant and then checking whether that constant would allow me to get over the height of the building

To find the spring constant you need the launch energy, and to find that you need to find the minimum speed that will get you over the building. Start with solving the trajectory.

 

[alphaQ]

To find the spring constant you need the launch energy, and to find that you need to find the minimum speed that will get you over the building. Start with solving the trajectory.

can you please give me an equation to get the launch energy?

 

[haruspex]

can you please give me an equation to get the launch energy?

As I wrote, you need to start by finding the trajectory.
You did not quote any relevant equations for that. Do you know what I mean by SUVAT equations? If not, look them up.