How to calculate the launch angle.?

Question

To find the launch angle when fireing water ballons (250g) for 30 meters away on the same plan. We where allowed to shoot two vertical shoots and we had the following results.Full catalpult extend 2.10m, the ballon took 4.3 seconds to hit the ground.Please can someone tell me how I need to work it out and to transfer all formulas onto excel.
Thanks

Answer 1

Assume no air resistance
the equations of motion are
x(t)=v0*cos(th)*t
where v0 is the initial speed leaving the launcher
y(t)=v0*sin(th)*t-.5*g*t^2

From the statement, you know that at impact 30 m from launch
30=v0*cos(th)*4.3
and
0=v0*sin(th)-.5*9.81*4.3
or
v0*sin(th)=.5*9.81*4.3

divide this by the horizontal impact equation to get

tan(th)/4.3=.5*9.81*4.3/30

or
th=atan(.5*9.81*4.3^2/30)

in Excel this will return an angel in radians. To get degrees use
th(degrees)=degrees(th)

This can be parametrized so you set up a cell for t and distance d
th=degrees(atan
(9.81*t^2/(2*d)))

j