- #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.