AP Physics

Unit 1 - Vectors and Kinematics

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Proportional Analysis

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Maximum Height Calculation

Step Formula Derivation Reasoning
1 [katex]v_{0y} = v_0 \sin(\theta)[/katex] Vertical component of initial velocity, where [katex]v_0 = 45 , \text{m/s}[/katex] and [katex]\theta = 29^\circ[/katex].
2 [katex]h_{\text{max}} = \frac{v_{0y}^2}{2g}[/katex] Maximum height formula, where [katex]g[/katex] is the acceleration due to gravity on Earth.
3 [katex]h_{\text{max, planet}} = 3.5 \times h_{\text{max}}[/katex] Maximum height on the distant planet is 3.5 times that on Earth.
4 [katex] \boxed{84.91 , \text{meters}} [/katex] Final Calculation

Range Calculation

Step Formula Derivation Reasoning
1 [katex]v_{0x} = v_0 \cos(\theta)[/katex] Horizontal component of initial velocity.
2 [katex]t = \frac{2v_{0y}}{g}[/katex] Time of flight formula on Earth.
3 [katex]R = v_{0x} \times t[/katex] Range formula on Earth, [katex]R[/katex] is the range.
4 [katex]R_{\text{planet}} = 3.5 \times R[/katex] Range on the distant planet is 3.5 times that on Earth.
5 [katex] \boxed{612.70 , \text{meters}} [/katex] Final Calculation

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