 #1
physicsdude2
 3
 0
 Homework Statement:
 For this assignment, I will need to launch a spring from a launcher at an angle of Θ. Given the following equations, I need to combine them to find x, the distance that the spring needs to be pulled back to hit the target (fall inside a box). The provided inputs for the launch are the horizontal distance from the target to the launcher, the vertical distance from the target to the launcher, and the angle that I will be launching the spring at.
 Relevant Equations:

The given equations are
Es=1/2(kx^2)
Eg=mgΔh
Ek=1/2(mv^2)
vh=vcosΘ
vv=vsinΘ
Δdh=vhΔt
Δdv=vvΔt+1/2(avΔt^2)
where vv is vertical velocity, vh is horizontal velocity, Δdv is vertical displacement, Δdh is horizontal displacement, t is time, x is the spring displacement (distance it needs to be pulled back, which is what i'm solving for), v is velocity, g is acceleration due to gravity (9.8m/s^2) and is also the same as av which is vertical acceleration, in this case 9.8 m/s^2 because this is dealing with projectile motion
I just need someone to check my calculations. There are no specific numbers, I just need a general equation. Look at my attached solution. I think I did everything right but the worrying detail is that gravitational energy is not included and I am not sure whether it should be.
Thanks in advance.
Thanks in advance.