Gravity Bucket Game

Projectile Motion Formula

Projectile Challenge:
Your goal: Find the firing angle and initial velocity to launch a cube so it clears the wall and lands in the bucket.
Given: The distance to the bucket (d) and the height of the wall (h_wall) are shown below. Gravity depends on the planet you choose.
What you must calculate:

• The firing angle (θ) in degrees
• The initial velocity (v) in m/s

Formula:
To land in the bucket: \( 0 = d \tan(\theta) - \frac{g d^2}{2 v^2 \cos^2(\theta)} \)
To clear the wall: \( y_{wall} = x_{wall} \tan(\theta) - \frac{g x_{wall}^2}{2 v^2 \cos^2(\theta)} > h_{wall} \)