What is the Initial Velocity and Angle of a Golf Ball Passing Over a 20m Tree?

[devanlevin]

a golf ball passes on its course exactly over the top of a tree standing 20m high and 40m away from the tee, the ball eventually lands 100m past the tree. what is the original velocity, speed and direction, of the stroke?

this is a question in kinematics and the only force to take into account is gravity,


using
V(t)=Vo+at
X(t)=Xo+Vot+½at²
V²-Vo²=2aΔx

Vx=const=cosθ*Vo
Vy(t)=sinθ*Vo+at

knowing that the ball passed through (40,20) i use the equation for X,
X(t)=40m=cosθ*Vo*t
t=40/cosθ*Vo

Y(t)=20m=sinθ*Vo*(40/cosθ*Vo)-4.9(40/cosθ*Vo)²
=40*tanθ-4.9(40/cosθ*Vo)²

now from here i don't know what to do, one equation with both values i need to find, θ and Vo, have i overlooked something, done something wrong or used the wrong equations for the case?

hope my english and the terms i used are correct, it is a question i have had to translate, thanks

 

[tiny-tim]

i don't know what to do, one equation with both values i need to find…

Hi devanlevin!

(btw, the English was fine, except just say "a golf ball passes exactly over the top of a tree …" )

Yes, you're right … you need one more equation …

you haven't used:

the ball eventually lands 100m past the tree

 

[devanlevin]

how can i work this into get an answer??

 

[tiny-tim]

how can i work this into get an answer??

Just do it!

You'll have two more equations, and only one more unknown (t2).

(it may … or may not … help to note that the maximum height is after 50 m horizontally)