Robin Hood has to shoot an arrow at an apple that sits on a wall 400 meters away, at a height of 40 meters. He must shoot at an angle of 60 degrees. What must the initial velocity of the arrow be to hit the target? Assume he's shooting laying down on the ground, making the arrow's inital height to be 0, and use -9.8 m/s² as the value of gravity.

Question

Steve · Answer

I'll assume he's lying on the ground... The arrow's height is

y = tanθ x - 4.9/(v cosθ)^2 x^2
so, we need

400√3 - 19.6*400^2/v^2 = 40
v = 69.309 m/s

y = √3 x - 4.9/(69.309/2)^2 x^2
see the graph at
http://www.wolframalpha.com/input/?i=plot+y%3D%E2%88%9A3+x+-+4.9%2F(69.309%2F2)%5E2+x%5E2,+y%3D40

unowen · Answer

Thanks for the help. But, he is LAYING down on the ground!!!!!!