Solving 2D Motion: Find Time & Velocity

[Atilla1982]

2d Motion

I've been stuck with this problem for a while. Appreciate if anyone can point me in the right direction.

A boy stands in a field, he throws a stone with an initial 45 degree angle. The field has a 5 degree angle downwards, so the stone touches down at -5 degree angle and 82 meters away. g=9,8m/s^2

Find the time (t) for the entire throw, and the initial velocity (v0) for the stone.

 

[Neverland]

sin45*v0*t=82*cos50
sin45*v0=g*t1
2*t1+t2=t
sin45*v0*t2+0.5*g*t2^2=82*sin50

4 equations for 4 unknows

we use the symmetry of the motion, and the independence of the motions in different directions

 

[Neverland]

sorry, cos50 and sin50 above mean cos5 and sin5

 

[Neverland]

and you can also use energy , but i don't think it woulb be much more easier

 

[Atilla1982]

couldn't i do: R=Vi^2*sin2(THETAi)/g

R=the length of the throw

Solving for Vi= 21.72 m/s

 

[Atilla1982]

And then set up an integral for time?