Human Cannonball Design Problem

[JohnStaporge]

Homework Statement

You are being hired by circus owner to design a cannon which will launch a human into the air toward a net 50 meters away (at the same height). THe design should conform to the following specifications (ignoring air resistance):

1. The circus tent has a maximum height of 30 meters.

2. In order to increase the dramatic effect, the human cannonball must be in the air for at least 3 seconds.

3. For "show" purposes, the launching angles should range somewhere between 30 and 60 degrees.

4. For safety reasons, the initials velocity should not exceed 31.3 m/s (70 mph). THis corresponds to approximately an 8g acceleration for 0.4 seconds.

5. You are to launch people with masses ranging between 50 and 80 kg.

I am to make an equation that will give the information below, using the rangesdescribed in the problem above:

1. Range (horizontal displacement when (change of y)=0).
2. The time of flight when (change of y)=0.
3. The maximum height for the flight.

Homework Equations

I was not given any equations to work with, but I am assuming that the following equations are significant:

R=(v0^2/g)xsin2θ
vy0=vy+gt
g=(v0^2/R)sin2θ

The Attempt at a Solution

Givens:
t>3 seconds
Angle= 30 degrees - 60 degrees
Vi < 31.3 m/s
Mass= 50kg - 80kg

I really don't know where to start ...

 

[JohnStaporge]

Can anyone just give me an idea on where to start?