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Home » \[ H = \frac(v_0 \sin \theta)^22g \] - Blask

\[ H = \frac(v_0 \sin \theta)^22g \] - Blask

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 \text{Slide down} = 12 - \sqrt{120} = 12 - 2\sqrt{30}

📌 But is \( \sqrt{120} = 2\sqrt{30} \)? Yes.

📌 \text{Decrease} = 12 - 2\sqrt{30}

📌 But wait — is this positive? \( 2\sqrt{30} \approx 2 \times 5.477 = 10.954 < 12 \), yes.

📌 So answer is \( 12 - 2\sqrt{30} \), but this is the amount it slides down — yes.

📌 However, the question is: "how far does the top of the ladder slide down?" — meaning the vertical distance it moves down:

📌 - \sqrt{120} = 12 - 2\sqrt{30}

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Factor out 9 from \( x \)-terms:
9(x^2 - 6x)
Complete the square:
x^2 - 6x = (x - 3)^2 - 9
Substitute back:
9((x - 3)^2 - 9) = 9(x - 3)^2 - 81
Complete the square for \( y \):
Factor out \(-16\) from \( y \)-terms:
-16(y^2 - 4y)
y^2 - 4y = (y - 2)^2 - 4

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