msoyland

@llama-life: 🧮 Step 1: Determine speed and landing angle Assumptions: You launch off the cliff horizontally (no upward or downward angle). The jump follows a parabolic trajectory due to gravity. Horizontal motion: 𝑥 = 𝑣 𝑥 ⋅ 𝑡 x=v x ​ ⋅t Horizontal distance 𝑥 = 30 x=30 m 𝑣 𝑥 v x ​ = constant horizontal speed Vertical motion: 𝑦 = 1 2 𝑔 𝑡 2 y= 2 1 ​ gt 2 Height 𝑦 = 25 y=25 m 𝑔 = 9.81   m/s 2 g=9.81m/s 2 🔹 Step 2: Time in the air From vertical formula: 25 = 1 2 ⋅ 9.81 ⋅ 𝑡 2 ⇒ 𝑡 2 = 50 9.81 ≈ 5.096 ⇒ 𝑡 ≈ 2.26  seconds 25= 2 1 ​ ⋅9.81⋅t 2 ⇒t 2 = 9.81 50 ​ ≈5.096⇒t≈2.26 seconds 🔹 Step 3: Horizontal speed 𝑣 𝑥 = 𝑥 𝑡 = 30 2.26 ≈ 13.27   m/s v x ​ = t x ​ = 2.26 30 ​ ≈13.27m/s 🔹 Step 4: Vertical speed upon impact 𝑣 𝑦 = 𝑔 ⋅ 𝑡 = 9.81 ⋅ 2.26 ≈ 22.17   m/s v y ​ =g⋅t=9.81⋅2.26≈22.17m/s 🔹 Step 5: Impact angle (landing slope) tan ⁡ ( 𝜃 ) = 𝑣 𝑦 𝑣 𝑥 = 22.17 13.27 ≈ 1.67 ⇒ 𝜃 ≈ arctan ⁡ ( 1.67 ) ≈ 59.4 ∘ tan(θ)= v x ​ v y ​ ​ = 13.27 22.17 ​ ≈1.67⇒θ≈arctan(1.67)≈59.4 ∘ ✅ Answer: The landing slope should be approximately 59 degrees down from horizontal to match your angle of descent.